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Man must rise above the Earth—to the top of the atmosphere and beyond—for only thus will he fully understand the world in which he lives.

— Socrates

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Syllabus of UPTU

EOE-034/EOE-044: SPACE SCIENCES

1. Introduction: Introduction to space science and applications, historical development

2. Solar System: Nebular theory of formation of our Solar System. Solar wind and nuclear reaction as the source of energy.

Sun and Planets: Brief description about shape size, period of rotation about axis and period of revolution, distance of planets from sun, Bode’s law, Kepler’s Laws of planetary motion, Newton’s deductions from Kepler’s Laws, Newton’s Law of gravitation, correction of Kepler’s third law, determination of mass of earth, determination of mass of planets with respect to earth. Brief description of Asteroids, Satellites and Comets.

3. Stars: Stellar spectra and structure, stellar evolution, nucleo-synthesis and formation of elements.

Classification of stars: Harvard classification system, Hertzsprung-Russel diagram, Luminosity of star, variable stars; composite stars (white dwarfs, Neutron stars, black hole, star clusters, supernova and binary stars); Chandrasekhar limit.

4. Galaxies: Galaxies and their evolution and origin, active galaxies and

quasars.

5. Creation of Universe:

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Early history of the universe, Big-Bang and Hubble expansion model of the universe, cosmic microwave background radiation, dark matter and dark energy.

Preface

Over Last few decades there have been exciting times for science in general and space science in particular. We have been able to probe the dense atmosphere of Venus. We think we have discovered the dying glow of big bang that began the expansion of the universe. We have identified the gravitational lenses in space, and we think we have found the black holes. We are thrilled with the discoveries from our exploration of solar system to find the dry rivers on Mars, volcanoes on the Jupiter’s satellite Io, rings around Jupiter, hundred of ringlets around the Saturn. We are able to map more than a dozen of new worlds in orbits about the giant planets of solar system with each comparable to our own Moon. The spacecrafts Voyager I and II have crossed the heliosphere. Further, we have been able to probe deep into the space by Hubble telescope which provides us the beautiful pictures of the objects. I am pleased that the interest in space science has increased manifold in last couple of decades. People are becoming more fervent in their desire to understand as much as they can about the cosmos and they are aware what space science can offer to human perspective. What they are not aware of is the method of science- of the exacting procedure and rigid rules of the scientific method. It is here there is a gap in communications that exists between scientist and nonscientist. The communication gap become obvious, when we notice that many people, have turned to all manner of unreliable sources for their information to satisfy their thirst for knowledge. As a scientist, we have an obligation to the public to increase our efforts in presenting the honest views of science. We must show not only how the universe is, but also how, by simple rational processes, we can probe its mysteries. We know that science has no pipeline to absolute knowledge; it can only interpret observed facts in terms of rules that seem to be revealed by objective analysis, therefore, science also has limitations. The book is designed to cover the syllabus of the UPTU. Various celestial processes and objects are described in detail

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with illustrations to clear the confusion between science and pseudoscience and give better understanding to the students. I have avoided mathematics beyond the simplest algebra throughout the text and have tried to stress that the space science is very human endeavor that is related to those men and women who created the science.The book is divided into nine chapters; we introduce the subject of space science in chapter 1. Solar system is described in chapter 2. The sun, the planets and satellites are discussed in chapter 3. Chapter 4 deals with the various laws of celestial mechanic. In chapter 5 we study stars and their common features. Chapter 6 deals with Stellar Evolution, while Final Stage of Stellar Evolution is discussed in chapter 7. In chapter 8 galaxies and various galactic processes are discussed. Finally, in chapter 9 we discuss the origin, evolution and other aspects of the universe.

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Acknowledgements

I would like to thank Mr. D. K. Gupta Founder cum Chairman, of Dr. R. N. Gupta Technical Education society and Anupama College of Engineering for his encouragement and allowing me to carry out this project, Dr. B. K. Gupta Secretary and Mr. Y. K. Gupta joint Secretary for their unflagging support.

I would like express my appreciation to my friend Dr. V. K. Jain for motivating to write this book, careful reading of the manuscript and his comments which have done much to improve it. I acknowledge the inspiration and blessings of my respected father in law Mr. V. N. Sharma.

Special thanks are due to my son Master Udbhav Garg whose many questions helped me to shape my thoughts properly.

A brief paragraph here cannot suffice to express my gratitude to my wife Anju Garg and Brother in law Mr. Mayank Sharma who has joined me to bring up this book by reading, correcting, criticizing and trying to make it more meaningful to you all. Loving care by my daughter Miss Ishita Garg is deeply appreciated.

Rajeev Garg

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Dedicated to my Parents

Late Mr. R. S. Garg & Omwati Garg

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Introduction to space science

Unit I

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Chapter 1Galileo Galilei (15 February 1564 – 8 January 1642) was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the

telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy, " the "father of modern physics, " the "father of science," and "the father of Modern Science. ” Stephen Hawking says, "Galileo, perhaps more than any other single person, was responsible for the birth of modern science."

Space Science

Four and half billion years ago, a rotating cloud of gaseous and dusty material on the fringes of Milky Way Galaxy flattens into disk, forming a star from the innermost matter. Collisions among dust particles orbiting a newly formed star, which humans call the sun, formed kilometer sized bodies called planetesimals, which in turn aggregated to form present day planets. On the third planet from the sun, several billions of years of evolution gave rise to a species of living beings equipped with intellectual capacity to speculate about the nature of the heavens above them.

Thousands of years ago, on this small rocky planet orbiting the sun in an ordinary spiral galaxy ancestor looked up and wondered about

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their place between the earth and sky. In twenty-first century people ask same profound question about how the universe began and evolved, how people got here, where they are going and whether they are alone in the universe. After only blink of an eye in cosmic time scale, those questions are beginning to be answered. In the last 60 years, space probes and space observatories have played central role in the progress of human exploration and development in understanding of space which is augmented by manned spacecrafts and space stations acting as the carriers of space equipments.

The seed of modern science began to sprout following the reformation. The 17th century German astronomer Johannes Kepler discovered for the first time certain simple mathematical rules that describe accurately the motions of the planets. His contemporary, the Italian physicist Galileo Galilei, discovered some other precise rules that described the behavior of bodies on the earth. Though the seeds of experimental science have been shown by certain of later Greek scholars, notably Archimedes, the practice of performing the experiments to learn the physical laws was not standard procedure even in Galileo’s time. Later in the same Seventeenth century, Isaac Newton showed that Kepler’s celestial rules and Galileo’s terrestrial ones are united by the same underlying Laws. Newton had the insight to recognize that the force that makes planets fall in ellipses about the sun and the force that makes apples fall with uniform acceleration near the earth’s surface are different manifestations of the same thing the gravitation.

The speculation on the nature of the universe must date from prehistoric times. It is difficult to state definitely when the earliest observations of a more or less quantitative sort were made or when astronomy as a science began. Certainly in many of the civilizations the regularity of motions of celestial bodies was recognized, and attempts were made to keep the track of and predict celestial phenomenon. It was thought that there is sort of unity between the heavens and the earth. To be sure, in classical Greece the earth was thought to be composed of base stuff- the four “elements”, the earth, water, air and fire- and heavens of crystalline material, the planets

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were gods, in some early cultures. And gods, presumably, control or influence the human affairs. By understanding the regularity in the motions in the heavens Ancients quite naturally understand the motions of their planet gods; they better understood the individual lots of men and women and sought a unity between the earth and heavens through primitive religion of astrology. Ironically, today in twenty first century enlightenment, a large fraction of all people still believe in that ancient religion. Thus the astronomy - the science involved with the observation, explanation and measuring of objects in outer space, began to develop to fulfill the human thirst of knowledge about heavens initiating the development in space science.

Astronomy compels the soul to look upward, and leads us from this world to another.

— Plato, The Republic, 342 BC

What is Space?

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines 'spaces' with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Many of the philosophical questions arose in the 17th century, during the early development of classical mechanics. In Isaac Newton's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was a collection of relations between objects, given by their distance and direction

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from one another. In the 18th century, Immanuel Kant described space and time as elements of a systematic framework which humans use to structure their experience. In 1905, Albert Einstein published a paper on a special theory of relativity, in which he proposed that space and time be combined into a single construct known as spacetime.

Thus we conclude that space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass); space can be explored via measurement and experiment.

Today the space science is an all-encompassing term that describes all the various science fields that are concerned with the study of the Universe, generally also meaning "excluding the Earth" and "outside of the Earth's atmosphere". Originally, all of these fields were considered part of astronomy. However, in recent years the major sub-fields within astronomy, such as astrophysics, have grown so large that they are now considered separate fields on their own. There are eight overall categories that can generally be described on their own; Astrophysics, Galactic Science, Stellar Science, non-Earth Planetary Science, Biology of Other Planets, Astronautics/Space Travel, Space Colonization and Space Defense.

The thrust in modern space science really began in 1946 when scientists first started to use balloons and sounding rockets to carry instruments to the outer fringes of the earth’s upper atmosphere. These efforts were followed by International Geophysical year in 1957-1958 when scientists planned to orbit satellites for their research. On October 4, 1957, when former Soviet Union launched sputnik-1 in the orbit, public reaction foster great efforts in space science by USA as an attempt to atone for cold war humiliation. As a result USA began to pour heretofore-undreamed resources into space science and hundreds of scientists shifted their research area to space science. In the year following World War II, the US scientific community turned its attention from the support of the war effort to

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scientific questions that has been the focus of attention before the war. The 1970 were the “golden age” of space science. In 1976 two Viking spacecrafts landed on the surface of the Mars and in 1977 two Voyager spacecrafts began their journey to Jupiter and Saturn and perhaps on to Uranus and Neptune.

1.1 The Astronomical methods

Astronomical methods are the equipment and techniques used to collect data about the objects in Space. Galileo's first astronomical method was to find and buy the best telescope of the time and then point that telescope to the heavens. Methods can be categorized according to the wavelength they are attempting to record.

Radio astronomy includes radio telescopes; devices that receive and record radio waves from outside the Earth. They record cosmic microwave background radiation resulting from the Big Bang, Pulsars and other sources. Optical astronomy is the oldest kind of astronomy. X-ray observatories include the Chandra X-ray Observatory and others; gamma ray includes the Compton Gamma Ray Observatory and others. Neutrino astronomy observatories have also been built, primarily to study our Sun. Gravitational wave observatories have been theorized. A space telescope is a telescope orbiting or traveling from the Earth, such as the Hubble space telescope. RXTE is Long Exposure Time Astronomy used to study millisecond pulsars and pulsar deceleration.

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Figure 1.1 Palomar Telescope.1.2 Descriptive astronomy

Galileo's second astronomical method was to describe what he saw in the telescope. Descriptive Astronomy is the highest sub-category of Astronomy to classify any knowledge related to describing celestial objects. Because we are seeing today portions of the Universe as they actually looked millions or billions of years ago we should have a historical section within descriptive astronomy: The history of the Universe includes the size, shape and structure of the historical universe, Cartography of The historical Universe, Early Universe and others. The Current Universe includes size shape and structure of the current Universe, cartography of the current Universe and others.

1.3 Cartography of Space Bodies.

Recording photographic or similar images of the Earths surface from space is a well developed science, yet still expanding because of advances in the actual resolution of images taken from space or atmosphere and because of advances in digitizing and manipulating the images. Most of these advances are being applied to the cartography of space-located bodies, even though acquiring the original images of those bodies is extremely complicated and expensive, usually requiring long distance probes to carry the cameras. Visible matter in the universe is apparently organized geographically into structures with large amounts of space between

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them; the space between planets, the space between stars or the space between galaxies. Even galaxies themselves are not spread uniformly but appear to be located in filaments. Therefore the Universe can be divided geographically into regions that follow this structure

1.3.1The Filaments of Galaxies 

They are the furthest visible structures made of superclusters, tending to line up in filaments. Our Milky Way Galaxy is a galaxy in what is called the Supercluster of Galaxies. It is some 150 million light-years across; and a great aggregation of perhaps thousands of smaller clusters of galaxies. The largest of these smaller clusters is called the Virgo Cluster. The Virgo Cluster contains the center of mass of Our Supercluster. Although The Milky Way Galaxy is a part of Our Supercluster, it is not a part of the Virgo Cluster. Our Milky Way Galaxy is part of a cluster called the Local Group. Gravitationally, our Local Group plays a small role in Our Supercluster because it is a small and distant cluster from the center. A much larger cluster within in Our Supercluster is the Ursa Major Cluster. The following objects are located within Our Supercluster but not within the Local Group; they are objects 100,000,000 light-years to 10,000,000 light-years from the Sun for example:  M49, M51, M58, M59, M60, M61, M63, M64, M65, and M66.

1.3.2 Local Group: Our Milky Way Galaxy is one of about 30 galaxies called the Local Group. The Local Group is about 4 million light-years across. In the Local Group our Milky Way Galaxy plays a large gravitational part because our galaxy is the second largest galaxy in our Local Group, second only to the Andromeda Galaxy. All of the other galaxies in our Local Group are gravitationally bound either to the Andromeda Galaxy or to our Milky Way Galaxy. Inside of our local group but outside of our Galaxy are objects 4,000,000 LY to

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1,000,000 LY from the Sun for example: M31, M32, and M33.

Figure 1.2 Image of the Orion and neighboring arms

1.3.3 Milky Way Galaxy: Our Milky Way Galaxy is massive mass-containing structure 100,000 light-years across and 30,000 light-years tall. Most of its billions of suns are organized into approximately 12 structures called "arms". Our Sun is located in what is called the "Orion Arm". The next arm outside of us is called the "Perseus Arm". The Crab Nebula M1 is located in the Perseus Arm. The arm outside of the Perseus Arm is called the Outer Arm. Palomar 1 is located in the Outer Arm. The next arm inside of us is called the Sagittarius Arm. The Ring Nebula M57 and the Carina Nebula (NGC 3372) are located in the Sagittarius Arm. The next arm inside of the Sagittarius Arm is called the Crux Arm. The inner arms are much shorter, obviously from being shifted by gravitational forces. Arms beside each other today may have at an earlier time been one. Orion Arm: The Orion Nebula M42 is located in our Arm. With Celestial Objects 1000 LY to 100 LY from the Sun for example: M39, M44, and M45. Celestial Objects 100 LY to 16LY From the

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Sun. Celestial Objects less than 16 LY from the Sun lies within this arm.

1.4 Nearby-Stars Solar Systems: By measuring the extremely small movements of nearby stars astronomers have been able to prove that there are planets going around these Suns, therefore these suns have become "Solar Systems”. Solar system  includes  Scientific Study of Solar System Planets, Venus, Mercury, Saturn, Jupiter, Uranus, Neptune, Mars, and Moon.

1.5 Physics of the universe / Astrophysics

After first looking at the planets, then describing what he saw, Galileo's third astronomical method was to theorize about the reasons for what he saw in the telescope, specifically to theorize that the Earth goes around the Sun? The Physics of the Universe can be divided into several broad categories:

(a) Astrophysical Theory That includes general relativity and others.

(b) Astrophysical Processes It includes baryonic and others physical processes that generally includes mechanics electromagnetism, electromagnetic forces, statistical mechanics, thermodynamics, quantum mechanics, relativity, gravity and others.

(c) Origins Of The Universe The theories of the Origins of the Universe, Big Bang Theory, Early Universe, Evidence, Cosmic Microwave Background, Dark Ages, etc are included in it.

(d) Interstellar Medium, voids, Filaments of Galaxies, galaxy clusters and others.

(e) Astrophysical Plasma It includes plasma and quasineutrality and others.

(f) Cosmic Plasmas between Stars, (Diffuse Plasmas) It includes intergalactic space, intergalactic medium, interstellar

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medium, interplanetary medium, heliosphere current sheet, interplanetary medium, Solar wind and others.

(g) Cosmic Plasmas inside Stars, (Dense Plasma) It includes Stars, active galactic nuclei, and fusion power, magnetohydrodynamic, X-rays, bremmstrahlung, Cosmology, recognized, ambipolar diffusion, Particle Physics and others.

1.6 Galactic Science /Cosmology

Physics can explain the underlying physical science of any galaxy, yet many aspects of galaxies are not best described through the physics. Galactic physical science is the general term for all physical sciences that can be applied to any galaxy in the Universe or to a particular galaxy.

(a) Galaxy Formation and Evolution includes galaxies, elliptical galaxies giant galaxies, spiral galaxies, M31 the Andromeda galaxy and others.

(b) Intra-Galactic Processes includes Black Hole, Globular Clusters, Satellite Galaxy, and Retrograde Rotation, Halo stars, High Velocity Clouds, Monoceros Ring, accretion disc, Gravitation, Angular momentum, Centripetal force, tidal effects, Viscosity, orbital momentum, Accretion disk, Active galactic nuclei, Protoplanetary discs, Gamma ray bursts and others.

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Figure 1.3 Galaxies in the Hubble Deep Field.

(c) Milky Way Galactic Physical Science is the overall science containing all the physical sciences related directly to the Milky Way Galaxy: Halo stars, Milky Way High Velocity Clouds, Milky Way Monoceros Ring, Milky Way accretion disc, Milky Way Gravitation, Milky Way Angular momentum, Milky Way Centripetal force, Milky Way tidal effects, Milky Way Viscosity, Milky Way orbital momentum, Milky Way event horizon, Milky Way black hole and others.

1.7 Stellar science

It is the general term for ALL physical sciences that can be applied to any star in the Universe or to a particular star it comprises of:

(a) Solar science of the Sun Sun is the overall science containing all of the physical sciences related directly to our local Sun.

(b) Stellar-Processes, General  Stellar dynamics, stars, Stellar Evolution, event horizon, black hole, x-rays, nuclear fusion and others. In astronomy, stellar evolution is the sequence of changes that a star undergoes during its lifetime; the hundreds of thousands, millions or billions of years during which it emits light and heat. Over the course of that time, the star will change radically. Stellar evolution is not studied by observing the life cycle of a single star—most stellar changes occur too slowly to be detected even over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars, each at a different point in its life cycle, and simulating stellar structure with computer models.

(c) Stellar evolution begins with a giant molecular cloud (GMC), also known as a stellar nursery. Most of the 'empty' space inside a galaxy actually contains around 0.1 to 1 particle per cm³, but

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inside a GMC, the typical density is a few million particles per cm³. A GMC contains 100,000 to 10,000,000 times as much mass as our Sun by virtue of its size: 50 to 300 light-years across.

Very small protostars never reach temperatures high enough or nuclear fusion of hydrogen to begin; these are brown dwarfs of less than 0.1 solar mass. Brown dwarfs heavier than 13 Jupiter masses (MJ) do fuse deuterium, and some astronomers prefer to call only these objects brown dwarfs, classifying anything larger than a planet but smaller than this a sub-stellar object. Both types, deuterium-burning or not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years. The central temperature in more massive protostars, however, will eventually reach 10 mega Kelvin, at which point hydrogen begins to fuse by way of the proton-proton chain reaction to deuterium and then to helium.

Figure 1.4 Quintuplet Cluster- Very young and near the Galactic Center.

The onset of nuclear fusion leads over a relatively short time to a hydrostatic equilibrium in which energy released by the core

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prevents further gravitational collapse. The star thus evolves rapidly to a stable state.

New stars come in a variety of sizes and colors. They range in spectral type from hot and blue to cool and red, and in mass from less than 0.5 to more than 20 solar masses. The brightness and color of a star depend on its surface temperature, which in turn depends on its mass.

A new star will fall at a specific point on the main sequence of the Hertzsprung-Russell diagram. Small, cool red dwarfs’ burn hydrogen slowly and may remain on the main sequence for hundreds of billions of years, while massive hot supergiants will leave the main sequence after just a few million years. A mid-sized star like the Sun will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its lifespan; thus, it is on the main sequence. Once a star expends most of the hydrogen in its core, it moves off the main sequence. It can be seen that on :

a. Maturity After millions to billions of years, depending on its initial mass, the continuous fusion of hydrogen into helium will cause a build-up of helium in the core. The later years and death of stars:

b. Low-mass star some stars may fuse helium in core hot-spots, causing an unstable and uneven reaction as well as a heavy solar wind. In this case, the star will form no planetary nebula but simply evaporate, leaving little more than a brown dwarf. But a star of less than about 0.5 solar mass will never be able to fuse helium even after the core ceases hydrogen fusion. There simply is not a stellar envelope massive enough to bear down enough pressure on the core. These are the red dwarfs, such as Proxima Centauri, some of which will live thousands of times longer than the Sun. Recent astrophysical models suggest that red dwarfs of 0.1 solar masses may stay on the main sequence for almost six trillion years, and take

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several hundred billion more to slowly collapse into a white dwarf.

c. Mid-sized stars once a medium-size star (between 0.4 and 3.4 solar masses) has reached the red giant phase, its outer layers continue to expand, the core contracts inward, and helium begins to fuse into carbon. In stars of less than 1.4 solar masses, the helium fusion process begins with an explosive burst of energy generation known as a helium flash. Helium burning reactions are extremely sensitive to temperature, which causes great instability. Huge pulsations build up, which eventually give the outer layers of the star enough kinetic energy to be ejected as a planetary nebula. At the center of the nebula remains the core of the star, which cools down to become a small but dense white dwarf, typically weighing about 0.6 solar masses, but only the volume of the Earth.

d. White dwarfs White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons. (This is a consequence of the Pauli Exclusion Principle.) With no fuel left to burn, the star radiates its remaining heat into space for thousands of millions of years. In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarf stars to exist.

e. Supermassive stars After the outer layers of a star greater than five solar masses have swollen into a gigantic red supergiant; the core begins to yield to gravity and starts to shrink. As it shrinks, it grows hotter and denser, and a new series of nuclear reactions begin to occur. These reactions fuse progressively heavier elements, temporarily halting the collapse of the core.

f. Neutron stars

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It is known that in some supernovae, the intense gravity inside the supergiant forces the electrons into the atomic nuclei, where they combine with the protons to form neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust motes, atoms would be as large as football stadiums), and the entire core of the star becomes nothing but a dense ball of contiguous neutrons or a single atomic nucleus.

g. Black holes it is widely believed that not all supernovae form neutron stars. If the stellar mass is high enough, the neutrons themselves will be crushed and the star will collapse until its radius is smaller than the Schwarzschild radius. The star has then become a black hole.

1.8 Earth planetary science

Figure 1.5 Solar System Planets.

The Earth and Planetary science includes the study of the following:

(a) Planetary Processes, Generally includes planetary science, Planets, Extrasolar Planet, Dwarf Planets, Comets, Asteroids and others.

(b) Geophysics is the study of the earth by quantitative physical methods, especially by seismic, electromagnetic, and radioactivity methods, therefore Planetary Geophysics is the study

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of the planets by quantitative physical methods, especially by seismic, electromagnetic, and radioactivity methods. It includes the branches of: Seismology (earthquakes and elastic waves), planetary gravity, geodesy, Tectonophysics (geological processes in the planets), Mineral Physics and others. Geophysics can be both a part of physics and a part of Geology.

(c) Geodesy of the Solar System, also called geodetics of the solar system, is the scientific discipline that deals with the measurement and representation of the planets of the Solar System, their gravitational fields and geodynamic phenomena (polar motion in three-dimensional, time-varying space. The science of geodesy has elements of both astrophysics and planetary sciences. The shape of the Earth is to a large extent the result of its rotation, which causes its equatorial bulge, and the competition of geologic processes such as the collision of plates and of volcanism, resisted by the Earth's gravity field. These principles can be applied to the solid surface of Earth (orogeny; Few mountains are higher than 10 km, few deep sea trenches deeper than that because quite simply, a mountain as tall as, for example, 15 km, would develop so much pressure at its base, due to gravity, that the rock there would become plastic, and the mountain would slump back to a height of roughly 10 km in a geologically insignificant time. Some or all of these geologic principles can be applied to other planets besides Earth. For instance on Mars, whose surface gravity is much less, the largest volcano, Olympus Mons, is 27 km high at its peak, a height that could not be maintained on Earth. The Earth geoid is essentially the figure of the Earth abstracted from its topographic features. Therefore the Mars geoid is essentially the figure of Mars abstracted from its topographic features. Surveying and  mapping are two important fields of application of geodesy. Physics is the underlying physical science of any planet, yet many aspects of planets are not best described through their physics. Planetary science is the general term for all physical sciences that can be applied to planets in the Universe or else to a particular planet.

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(d) Planetary science of the Earth is the overall physical science containing all the physical sciences related directly to our Earth. Planetary Science can be broadly divided into several major sciences: Geology, Oceanography and Atmospheres.

(e) Geology of Solar System Planets contains geology of Mercury, geology of Venus, geology of the Moon, geology of Mars, geology of Jupiter, geology of Saturn, geology of Uranus, geology of Neptune, and geology of Pluto

(f) Geology of Other Planets Planetary geology (sometimes known as Astrogeology) refers to the application of geologic principles to other bodies of the solar system. However, specialized terms such as selenology (studies of the  Moon), areology (of Mars), etc., are also in use. Most of the geological sciences related to the Earth can be directly applied to the study of non-Earth planets:

(g) Geology Fields or related disciplines Structural geology, Geomorphology., Economic geology,  Mining geology, Geodetics, Geomorphology, Geophysics, Historical geology, Hydrogeology or geohydrology, Mineralogy, Paleoclimatology, Sedimentology,  Seismology,  Stratigraphy,  Structural geology, Volcanology, Hydrology, Geothermometry (heating of the earth, heat flow, volcanology, and hot springs), Hydrology (ground and surface water, sometimes including glaciology).

(h) Extrasolar Geology is currently a young science because only recently have extrasolar planets been found.

(i) Atmospheres of Solar System Planets refers to the application of meteorological principles to other bodies of the solar system including the application of: Atmospheric electricity and terrestrial magnetism (including ionosphere, Van Allen belts,  telluric currents, Radiant energy, etc.), Meteorology and Climatology. Aeronomy the study of the physical structure and chemistry of the atmosphere. Atmosphere of Planets of the Solar System that includes Mars atmosphere, Jupiter atmosphere, atmosphere on Jupiter’s-Moons,

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atmosphere, atmosphere on Uranus and atmospheres of Extrasolar Planets is currently a young science because only recently have extrasolar planets been found. Astronomers are currently theorizing that the recently discovered extrasolar Jupiter-sized planets have continuous surface winds of many thousands of miles per hour caused by their highly elliptical orbit which brings them close to their parent star.

(j) Planets around other stars

Figure 1.6 Planets around other stars

Over the last few years, intensified research and improved observational techniques have led to the discovery of stars which are orbited by companions of very low mass.  The data so far available indicate that at least the majority of these have masses comparable to that of Jupiter, the largest planet in our own solar system. Efforts to discover more planetary companions to other stars in the Milky Way galaxy are being vigorously pursued and will no doubt feature prominently in astronomical research over the next several decades.

The International Astronomical union (IAU) provides a forum for international discussion and coordination of research in this exciting new branch of astronomy.

In order to facilitate international research in the field, and as part of these discussions, the IAU is also developing a system for clear and unambiguous scientific designation of these bodies at all stages

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during their study, from tentative identification to fully-characterized objects.  Such a system must take into account that discoveries are often tentative, later to be confirmed or rejected, possibly by several different methods, and that several planets belonging to the same star may eventually be discovered, again possibly by different means.  Thus, considerable care and experience are required in its design.

In response to frequent questions about plans to assign actual names to extra-solar planets, the IAU sees no need and has no plan to assign names to these objects at the present stage of our knowledge.  Indeed, if planets are found to occur very frequently in the Universe, a system of individual names for planets might well rapidly be found equally impracticable as it is for stars, as planet discoveries progress.

1.9 Exobiology / Extraterrestrial life

Earth telescopes can resolve some surface features of the nearby planets and so far, no life can be seen through the telescopes. However, Earth telescopes cannot resolve the surface features of any planet outside the solar system, so the search for life on other planets continues. While no incontestable evidence has been found for life outside of Earth, the scientific study of the theoretical basis for life on other bodies is progressing. Some scientists are trying to theorize which kinds of stars would have planets that hold life. Because life has overall fragile parameters for survival the general consensus is that only older stars would have planets circling them with life. From this they theorize which sections of our Milky Way Galaxy would most likely hold life. Other scientists theorize the quantity of civilizations that might exist in a galaxy and others are actually listening for the possible radio chatter of extraterrestrial technical civilizations. These sub-sciences of exobiology can be categorized as follows:

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Figure 1.7 Silicon Based Life-A picture of silent, the silicon-based analogue of methane.

(a) Habitable Zone Astrobiology is discussed in Galactic Habitable Zone and Solar System Habitable Zone.

(b) Astrobiochemistry Exogenesis most scientists hold that if extraterrestrial life exists, its evolution would have occurred independently in different places in the universe. An alternative hypothesis, held by a minority, is panspermia, which suggests that life in the universe could have stemmed from a smaller number of points of origin, and then spread across the universe, from habitable planet to habitable planet. These two hypotheses are not mutually exclusive. Alternative biochemistry includes Alternative Carbon Biochemistry where water is not the Solvent of Carbon Chains: Life forms based in ammonia rather than water are also considered, though this solution appears less optimal than water Also included is Alternative Non-Carbon Biochemistry- non-carbon based chemistry  Silicon is usually considered the most likely alternative to carbon, though this remains improbable. Silicon life forms are proposed to have a crystalline morphology, and are theorized to be able to exist in high temperatures, such as planets closer to the sun.

(c) Astrobiosphere is the entire area of a planet that supports life and includes Biosphere, Theory of Biosphere, Planetary

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Habitability Extrasolar planets Astronomers also search for extrasolar planets that would be conducive to life, especially those like OGLE-2005-BLG-390Lb which have been found to have Earth-like qualities.

(d) Plants On Other Planets  includes  Extremophiles, Theoretical Astrobotany, Life On Jupiter, Life on Mars scientific theory, Independently in 1996 structures resembling bacteria were reportedly discovered in a meteorite, ALH84001, thought to be formed of rock ejected from Mars. This report is also controversial and scientific debate continues.

(e) Humanoids-On-Other-Planets include Humanoids – On - Other S-Planets Origins- Speculations and Scientific Theory Panspermia. Extraterrestrial life along with the biochemical basis of extraterrestrial life, there remains a broader consideration of evolution and morphology.

(f) Humanoids- On- Other- Planets Technical Civilizations includes Humanoids – On – Other – Planets, Technical - Civilizations, Speculation and theory. Most scientists hold that if extraterrestrial life exists, its evolution would have occurred independently in different places in the universe. An alternative hypothesis, held by a minority, is panspermia, which suggests that life in the universe could have stemmed from a smaller number of points of origin, and then spread across the universe, from habitable planet to habitable planet.

(g) Humanoids-On-Other-Planets-Civilizations on Local Stars includes Search for Humanoids-On-Other-Planets-Civilizations on Local-Stars.

1.10 Space Exploration through space travel

Astronomy is exploration of space through instruments based on Earth. Space Exploration through space travel is exploration of space by travel through it, either in person or by drone. Closely associated with Space travel is Space Station, either manned or unmanned. All

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man-made satellites are a form of unmanned or manned space stations

(a) Unmanned Space travel includes the sciences of Spacecraft Propulsion, Rocket launch technology, Rocket, Astrodynamics, Unmanned space missions, and others.

(b) Manned Space travel further includes the sciences of Microgravity environment, Space transport, manned space missions, interplanetary travel, Interstellar travel and Generation ship.

(c) Unmanned space station There are Astronomical satellites, Biosatellites, Communications satellites, miniaturized satellites, Navigation satellites, Reconnaissance satellites, Earth observation satellites, Earth observation satellites and others. There are many different kinds of orbits possible for these devices.

(d) Manned Space Station includes the sciences of Space Station and Floating cities.

Figure 1.8 Orion approaching the ISS.

1.11 Space colonization

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Space colonization is a colossal science that includes all of the scientific disciplines needed to be able to build colonies on non-Earth planets and planetoids.

(a) Space Colonization Justification includes the sciences of Space and survival.

(b) Space Colony Research And Development Man can practice living on other worlds by building permanently inhabitable cities in extremely hostile environments of the Earth: The poles and the deserts. Currently manned Earth hostile-environment stations include Amundsen-Scott South Pole Station, Devon Island, Mars Arctic Research Station, Mars Desert Research Station, climate, underwater structures for planets with oceans or very heavy atmospheres and others.

(c) Space Colony Location is the science of figuring out the best planets and the best locations on those planets for colonization. Because water is such a necessity for human survival most searches are for locations close to some kind of water. In the planets such as Mars Colonization,  Colonization of Mercury, Colonization of Venus, Venusians terraforming, Colonization of the Moon,  Artemis Project, Europa, Phobos, colonization of the asteroids and others.

(d) Space Colonization Habitat science includes Space habitat, Human adaptation to space, Manmade closed ecological system, planetary habitability, domed city, Ocean colonization, Underground city and other sub-sciences.

(e) Space Colonization Agriculture includes Biosphere 2 and BIOS-3 and others.

(f) Space Colonization Food Processing includes Space food and others.

(g) Space Colonization Housing includes International Space Station.

(h) Space Colonization Clothing includes Space suits.

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(i) Space Colonization Construction includes Orbital Mega structures, station-keeping, Amundsen-Scott South Pole Station, Devon Island, Mars Arctic Research Station, Mars Desert Research Station, climate, underwater structures for planets with oceans or very heavy atmospheres and others.

(j) Space Colonization Transportation includes lunar rover.

(k) Space Colonization Materials includes Recycling.

(l) Space Colonization Energy includes Renewable energy.

(m) Space Colonization General Manufacturing includes Space Manufacturing.

(n) Space Colonization Economics: includes Space Frontier Foundation, Private space flight and space tourism, solar power satellites, Asteroid mining, space manufacturing,

(o) Space Colonization Operations: includes space agencies, Space advocacy, Colonize the Cosmos, Artemis Project, National Space Society, Planetary Society, robotic exploration, search for extraterrestrial life. 

1.12 Space Defense

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Figure 1.9 Space Lasers.

Space Defense is the science of defending the Earth from natural or unnatural threats from Space. Natural threats include Near Earth Asteroids and similar. Other issues are discussed in Missile Defense Command, United States Army Space and Missile Defense Command, Department of Defense Manned Space Flight Support Office, European Aeronautic Defense & Space and Joint Defense Space Research Facility.

1.13 Applications of Space Science

(a) Space technology can be used to support the disaster management by use of the earth observation satellites accurate picture of the damage can be obtained.

(b) Global Navigational Satellite System (GNSS) are space based radio positioning systems that provide round the clock three dimensional positions, velocity and time information to suitably equipped users anywhere on or near the surface of the earth. It makes significant contribution in the areas of aviation, land and maritime transportation, mapping and surveying, precision

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agriculture, power and telecommunications networks, disaster warnings and emergency response.

(c) Communication satellites have the potential of bridging “the knowledge gap” between rich and poor countries by leapfrogging certain stages of developments, by improving education, health services and promoting favorable conditions for environmental protection.

(d) Natural resource assessment can be done by using GIS layers.(e) Space technology has improved vastly the Broadcasting, tele-

education, tele-medicine services.

Summery

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.

Space is one of the few fundamental quantities in physics

In the last 60 years, space probes and space observatories have played central role in the progress of human exploration and development in understanding of space.

The thrust in modern space science really began in 1946 and the 1970 were the “golden age” of space science.

The space science is an all-encompassing term that describes all the various science fields that are concerned with the study of the Universe.

Astronomical methods are the equipment and techniques used to collect data about the objects in Space.

The Physics of the Universe can be divided into several broad categories.

There are eight overall categories in space science that can generally be described on their own; Astrophysics, Galactic Science, Stellar Science, non-Earth Planetary Science, Biology of Other Planets, Astronautics/Space Travel, Space Colonization and Space Defense.

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Space technology can be used Broadcasting, tele-education, tele-medicine services, and disaster management etc.

Exercises

Fill in the blanks

1. ______ cannot be defined via other quantities because nothing more fundamental is known at the present.

2. The 1970 were the _______________ of space science.

3. The space science is a ______________ term that describes all the various ___________ fields that are concerned with the study of the Universe.

4. There are _________ overall categories in space science that can generally be described on their own.

5. The equipment and techniques used to collect data about the objects in Space is called ________________.

6. ___________________ is Galileo's second astronomical method was to describe what he saw in the telescope.

7. Most of the 'empty' space inside a galaxy actually contains around _______ to ______particle per cm³.

8. Space ____________ is a colossal science that includes all of the ____________disciplines needed to be able to build colonies on non-Earth planets and planetoids.

9. Space Defense is the science of defending the Earth from natural or __________threats from Space.

10. _____________ is the entire area of a planet that supports life and includes Biosphere.

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Short questions with answerQ1. What do you understand by space science?Ans. Today the space science is an all-encompassing term that

describes all the various science fields that are concerned with the study of the Universe, generally also meaning "excluding the Earth" and "outside of the Earth's atmosphere".

Q2. How exploration and development in our understanding of space augmented?

Ans. In the last 60 years, space probes and space observatories have played central role in the progress of human exploration and development in understanding of space which is augmented by manned spacecrafts and space stations acting as the carriers of space equipments.

Q3. What was the golden period of space science?

Ans. The 1970 were the “golden age” of space science. In 1976 two Viking spacecrafts landed on the surface of the Mars and in 1977 two Voyager spacecrafts began their journey to Jupiter, Saturn, Uranus, and Neptune and beyond heliosphere.

Q4. What are the major subfields within astronomy?Ans. The major sub-fields within astronomy, such as astrophysics,

have grown so large that they are now considered separate fields on their own. There are eight overall categories that can generally be described on their own; Astrophysics, Galactic Science, Stellar Science, non-Earth Planetary Science, Biology of Other Planets, Astronautics/Space Travel, Space Colonization and Space Defense.

Q5. What was Galileo’s first method of astronomy?Ans. Galileo's first astronomical method was to find and buy the best

telescope of the time and then points that telescope to the heavens.

Q6. What is the role of Milky Way in its Local Group?Ans. In the Local Group our Milky Way Galaxy plays a large

gravitational part because our galaxy is the second largest

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galaxy in our Local Group, second only to the Andromeda Galaxy.

Q7. What is stellar evolution?Ans. It is the sequence of changes that a star undergoes during its

lifetime.Q8. What are brown dwarfs?Ans. A very small protostars where temperatures never reach high

enough or nuclear fusion of hydrogen cannot begin is brown dwarfs of less than 0.1 solar mass. In brown dwarfs heavier than 13 Jupiter masses (MJ) there is a fusion to deuterium, and some astronomers prefer to call only these objects brown dwarfs, thus, classifying anything larger than a planet but smaller than this a sub-stellar object as brown dwarfs.

Q9. What is main sequence star?Ans. It is the sequence of changes that a star undergoes during its

lifetime.Q10. What is stellar evolution?Ans. It is the sequence of changes that a star undergoes during its

lifetime.Q11. What is the main factor to ignite helium burning in a star?Ans. Temperature is the main factor to ignite helium burning in a

star.

Study QuestionsQ1. Define Space? Write a note on its development?Q2. Discuss Astronomical Methods?

Q3. What do you understand with cartography of space bodies?

Q4. Discuss the various processes of stellar science?

Q5. What is the importance of Exobiology?

Q6. Describe Space colonization?Q7. What you understand with Geodesy of the Solar System?Q8. What is the importance of space travel?Q9. Give some of the applications of space science?Q10. How Space travel is important in the exploration of the space?

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Solar System

Unit II

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Chapter 2

Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a renaissance  astronomer   and the first to formulate a comprehensive heliocentric cosmology, which displaced the Earth from the center of the universe.

Solar System

In ancient times the earth was considered to be the central and dominant in the universe, while the sun, moon and planets were considered to be luminous orbs that moved about on the celestial sphere through the zodiac. However, our solar system is indeed dominated by one body the sun, not the earth. The sun though very important to us is an ordinary star. Only careful scrutiny at a close range would reveal the tiny planets to an imaginary interstellar visitor. First the Jupiter, the largest, would be seen; then Venus and Saturn; and perhaps only with the greatest difficulty, the earth and other planets. Almost 99.99 percent of the matter in the system is the sun itself; the planets comprise most of what is left- the earth scarcely counts among them. The countless millions of other objects in the solar system, mostly unknown to ancients would probably remain unnoticed by a casual traveler passing through solar neighborhood.

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For many thousands of years, humanity, with a few notable exceptions, did not recognize the existence of the Solar System. They believed the Earth to be stationary at the centre of the universe and categorically different from the divine or ethereal objects that moved through the sky. Although the Indian mathematician-astronomer Aryabhata and the Greek philosopher Aristarchus of Samos had speculated on a heliocentric reordering of the cosmos, while Nicolaus Copernicus was the first to develop a mathematically predictive heliocentric system. His 17th-century successors, Galileo Galilei, Johannes Kepler and Isaac Newton, developed an understanding of physics which led to the gradual acceptance of the idea that the Earth moves around the Sun and that the planets are governed by the same physical laws that governed the Earth. In more recent times, improvements in the telescope and the use of unmanned spacecraft have enabled the investigation of geological phenomena such as mountains and craters, and seasonal meteorological phenomena such as clouds, dust storms and ice caps on the other planets.

2.1 Inventory of Solar System

The Solar System consists of the Sun and those celestial objects bound to it by gravity, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. Of the retinue of objects that orbit the Sun, most of the mass is contained within eight relatively solitary planets whose orbits are almost circular and lie within a nearly-flat disc called the ecliptic plane. The four smaller inner planets, Mercury, Venus, Earth and Mars, also called the terrestrial planets, are primarily composed of rock and metal. The four outer planets, Jupiter, Saturn, Uranus and Neptune, also called the gas giants, are composed largely of hydrogen and helium and are far more massive than the terrestrials.

The Solar System is also home to two regions populated by smaller objects. The asteroid belt, which lies between Mars and Jupiter, is similar to the terrestrial planets as it is composed mainly of rock and

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metal. Beyond Neptune's orbit lie trans-Neptunian objects composed mostly of ices such as water, ammonia and methane. Within these regions, five individual objects, Ceres, Pluto, Haumea,  Makemake and Eris, are recognized to be large enough to have been rounded by their own gravity, and are thus termed dwarf planets. In addition to thousands of small bodies in those two regions, various other small body populations, such as comets, centaurs and interplanetary dust, freely travel between regions.

The solar wind, a flow of plasma from the Sun, creates a bubble in the interstellar medium known as the heliosphere, which extends out to the edge of the scattered disc. The hypothetical Oort cloud, which acts as the source for long-period comets, may also exist at a distance roughly a thousand times further than the heliosphere.

Six of the planets and three of the dwarf planets are orbited by natural satellites, usually termed "moons" after Earth's Moon. Each of the outer planets is encircled by planetary rings of dust and other particles.

The relative prominence of various kinds of members of solar system is indicated in Table 2.1 which lists the approximate distribution of mass among the bodies of solar system. The last four entries in the table are order of magnitude guesses only.

Object Percentage of MassSun 99.85

Planets 0.135Comets 0.01 (?)

Satellites 0.00005Minor Planets 0.0000002 (?)

Meteoroids 0.0000001(?)Interplanetary medium ‹‹ 0.0000001

Table 2.1 Distribution of Mass in Solar System

2.2 Origin of Solar System

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Analysis of rocks in the earth and moon and of meteorites revels that the oldest of them all have ages of about 4500 million years. The theoretical studies of the early evolution of sun suggest the age of the sun to be same. Thus we can say our solar system was formed slightly less than 5000 million years ago. Further the organization of planets in the solar system is quite orderly. They all lie nearly in same plane with orbits nearly circular in shape and are regularly spaced. All the planets revolve in the same direction – from west to east (same as the direction of rotation of the sun). Most of the planets and most of the satellites of the planets rotate from west to east as well. These facts alone rule out once popular catastrophic theory of origin of solar system. According to this theory, a passing star pulled out the matter from the sun that later condensed into planets. Any matter so extracted even if it were not lost to solar system, could hardly have formed into planets with regularly spaced near circular orbits, and hot gases would have been dispersed, not formed into planets. Moreover, such close encounters of passing stars are exceedingly rare.Today it is generally accepted that the sun and planets formed together from the same original tenuous cloud of interstellar gas and dust called solar nebula. The idea appears to have been first suggested by the German philosopher Immanuel Kant, in mid 18th

Century, and was developed into the specific model by French astronomer Marquis Pierre Simon de Laplace near the end of same century. This Kant- Laplace idea is known as nebular hypothesis. This Kant –Laplace model cannot be correct in detail, but the modern versions are consistent with well known laws of mechanics. There is broad general agreement on the broad outline of the formation of the solar system; however its details are uncertain and are still rather speculative- not because of the subject is particularly mysterious but because we simply do not yet have enough information to choose among the models.

In the nebula model it is assumed that about 5000 million years ago the solar system condensed from a tenuous cloud of gas and dust formed the solar nebula having the diameter thousands of times that of orbit of most distant present planet- perhaps as much as a light year or so It would have to have had some original net rotation probably due to differential rotation of the Galaxy itself. The rotation of the original cloud has been exceedingly slight-merely a slight net

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unbalance of the many random motions of the gases within it. It is seen that some stars eject matter into space. Thus the interstellar medium from which our solar system is condensed was not simply the left over matter that did not condensed into star when the Galaxy was formed, but also it contains a good deal of matter that was formerly part of another star.

Most stars derive their energy by thermonuclear conversion of light atoms into heavier ones, thereby slowly changing their chemical composition. The solar nebula therefore, contained many atoms that have been built up by nuclear reactions of another stars. It may be noted that our own bodies are made up of atoms, many or most of which are formed in earlier stars. The solar nebula so formed perhaps represented a fluctuation of density, so that it was very slightly denser than the gas in the interstellar medium surrounding it. Thus it must have been gravitationally unstable so that its gravitation was enough to pull its parts together, that is, the random motion of its gaseous parts and dust particles were great enough for them to escape each other dispersing the cloud, so it began to contract under its own gravity. As it contracted, it has to conserve the angular momentum which force it to rotate faster and faster as it draw itself together .After some time the rotation began to produce orderly structures. Eventually, the matter in the outer equatorial region of the rotating cloud, moving ever faster as it contracted, had a high enough speed to stay in a circular orbit about the center of mass of cloud. The material in that part of nebula could not come any closer to the center. To do so it would have to speed up still more (to conserve angular momentum); an increase in speed, however would force it to move out away from the center into larger orbit, and there was no energy available to move it out against the pull of gravity. Thus the material in the equatorial region was simply left behind in roughly circular orbit as the rest of the cloud continued to fall inward. As the time went on more and more material was left behind the shrinking cloud, moving in a circular orbits and forming a disk of materials. The matter in the disk could no longer contract towards its center, although matter on either sides of the disk could fall towards it (falling towards disk in the direction parallel to the axis of rotation).In this way rotating solar nebula flattened itself into disk.

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The in falling atoms picked up speed as they fall, and when the gas density become high enough for them to collide with each other, the kinetic energy was distributed among atoms becoming heat. Most of this heat was radiated away from the disk, but in central condensation- to become the sun-the density grow until gases of the gases of the protosun become opaque. The opacity trapped the heat inside and the pressure produced by heat slowed down the contraction. The shrinking nebula had become a great globe of hot gases that could contract only very gradually, as it was able to slowly radiate away the heat trapped in the interior .Thus a star (the sun) was born at the center, containing perhaps half or more of the material of the original cloud. The rest of the nebula was in the form of a relatively cold rotating disk, from which the planets and their satellites ware formed.

In the inner part of solar nebula the high luminosity of young sun would have evaporated the gases that were composed of volatile substances. Thus Particles of water ice and frozen carbon di oxide could exist only far away out in the disk. Rocks and the metallic grains, on the other hand, could survive throughout the disk. In all parts of that rotating disk, though, the orbiting particles were constantly colliding and often sticking together, and many grow by accretion. A few began to get big enough to gravitationally affect those which come near. Sometimes the smaller particles would pass close enough to the bigger one to bump into them and stick. But if they do not pass close enough to hit; they could be gravitationally deflected to the another part of the disk, or even out of solar system altogether

In this way, a few large chunks gradually won out over their neighbors, either capturing them or getting rid of them thereby sweeping out ring shaped swaths in the solar nebula all centered on the sun. They become planets. In the final stage of this accretion the young planets swept up the last of the solid chunks remaining on the disk. There must have been many craters producing explosions as these chunks smashed home on the planets without dense atmospheres. We can still observe the heavy catering produced in this period.

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The planets in the inner part of the solar system Mercury, Venus, Earth and Mars build up of rocky and metallic particles. They have lot in common and are called the terrestrial (earth like) planets. They could attract and hold on to none of the gases in the solar nebula. Their present atmospheres have out gassed from rocks beneath their surfaces; Mercury however, is too small to retain even this kind of atmosphere.

Far out in the nebula, on the other hand, it was cool enough for grains to exist; along with rocky and metallic ones. The planets that accreted out there Jupiter, Saturn Uranus and Neptune formed out of lots of ices as well as rocks and metals. They have lot in common, and are called Jovian (Jupiter like) planets. Jupiter and Saturn were large enough to even attract and hold a large amount of gases in the solar nebula. Jupiter in particular, has the present composition almost like that of the sun; it is mostly the hydrogen and helium.

The favored theory of the origin of moon is that it and the earth formed together, the moon accreting from the material in the orbit about the primordial earth. Some, theorists, however, argue that the moon and earth could have formed independently in different parts of the solar nebula but at the same distance from the sun. In this case earth and moon would have to have been trapped in each others mutual gravitational field at later time. Most of the other planets have satellites, and many of them are believed to have formed by accretion from the material in the orbit about their parent planets. Some satellites however, such as the outer ones of Jupiter, have eccentric orbits and even revolve from east to west (opposite to the revolution of the planet and most of the satellites) these were probably captured after their formation.

The Asteroids may simply be the objects that never accreted to single large planets, perhaps because there were too little mass in that part of solar system to begin with or perhaps due to the tidal influence of Jupiter. They may however, be still fragmenting by collisions and have started from a much smaller original number of bodies. Planets and minor members of the solar system contribute only minutely to its total mass. The original mass of the disk must have been much

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greater, for it is doubtful if practically all of the solar nebula could be condensed into the sun itself. We know when a star first began to shine it is temporarily much more luminous than when it is fully developed. In that period of the Sun’s existence a large flux of energy from it both in form of photons and corpuscular radiation (atomic nuclei and electrons) may have interacted with uncondensed gases and tiny unaccerted particles and “blown” them from solar system. Such an early solar winds of corpuscular radiation could also have carried away most of the sun’s angular momentum comprises only about 2 percent of that of solar system, despite the fact that the sun has more than 99.8 percent of the systems present mass. The study of stars has indicated that all stars are not formed in the manner the sun was formed. Often, the original protostar fissions into two condensations to become a double star, and the original angular momentum are conserved in the orbital motions of two stars rather than in one star with the system of planets. Other times the cloud breaks up into cluster of stars. We don’t know how often planetary systems are formed. At most it’s only half the times, because about half the stars around us are member of binary star systems. Some recent studies have indicated that the formation of planetary systems might be relatively rare.

Figure 2.1 Schematic representation of the formation of the solar system(1) the solar nebula condensed from the interstellar medium and contracts (2) as the nebula shrinks its rotation causes it to flatten, until (3) the nebula is a disk of matter with the concentration near the center, which (4) becomes the primordial sun. Meanwhile, solid particles condense to the inner solar nebula. These (5)

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accrete to form the terrestrial planets. The pressure of radiation and wind of corpuscular radiation from the primordial sun blow the solar system clean of most of the matter in the disk that did not form into the planets. The figures are not to the same scale, the original nebula has to contract greatly before its rotation produces appreciable flattening.

2.3 The Structure of Solar System

The principal component of the Solar System is the Sun, a main sequence G2 star that contains 99.86 percent of the system's known mass and dominates it gravitationally. The Sun's four largest orbiting bodies, the gas giants, account for 99 percent of the remaining mass, with Jupiter and Saturn together comprising more than 90 percent.

Most large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic. The planets are very close to the ecliptic while comets and Kuiper belt objects are frequently at significantly greater angles to it. All of the planets and most other objects also orbit with the Sun's rotation (counter-clockwise, as viewed from above the Sun's North Pole). There are exceptions, such as Halley's Comet.

To cope with the vast distances involved, many representations of the Solar System show orbits the same distance apart. In reality, with a few exceptions, the farther a planet or belt is from the Sun, the larger the distance between it and the previous orbit. For example, Venus is approximately 0.33 astronomical units (AU) farther out from the Sun than Mercury, while Saturn is 4.3 AU out from Jupiter, and Neptune lies 10.5 AU out from Uranus. Attempts have been made to determine a correlation between these orbital distances (for example, the Titius-Bode law), but no such theory has been accepted.

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Figure 2.2 The orbits of the bodies in the Solar System to scale (clockwise from top left)

Kepler's laws of planetary motion describe the orbits of objects about the Sun. According to Kepler's laws, each object travels along an ellipse with the Sun at one focus. Objects closer to the Sun (with smaller semi-major axes) have shorter years. On an elliptical orbit, a body's distance from the Sun varies over the course of its year. A body's closest approach to the Sun is called its perihelion, while its most distant point from the Sun is called its aphelion. Each body moves fastest at its perihelion and slowest at its aphelion. The orbits of the planets are nearly circular, but many comets, asteroids and Kuiper belt objects follow highly elliptical orbits.

Most of the planets in the Solar System possess secondary systems of their own. Many are in turn orbited by planetary objects called natural satellites, or moons, some of which are larger than the planet Mercury. Most of the largest natural satellites are in synchronous rotation, with one face permanently turned toward their parent. The four largest planets, the gas giants, also possess planetary rings, thin bands of tiny particles that orbit them in unison.

2.4 Terminology

Informally, the Solar System is sometimes divided into separate regions. The inner Solar System includes the four terrestrial planets and the main asteroid belt. The outer Solar System is beyond the

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asteroids, including the four gas giant planets. Since the discovery of the Kuiper belt, the outermost parts of the Solar System are considered a distinct region consisting of the objects beyond Neptune.

Dynamically and physically, objects orbiting the Sun are officially classed into three categories: planets, dwarf planets and small Solar System bodies. A planet is any body in orbit around the Sun that has enough mass to form itself into a spherical shape and has cleared its immediate neighborhood of all smaller objects. By this definition, the Solar System has eight known planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Pluto does not fit this definition, as it has not cleared its orbit of surrounding Kuiper belt objects. A dwarf planet is a celestial body orbiting the Sun that is massive enough to be rounded by its own gravity but which has not cleared its neighboring region of planetesimals and is not a satellite. By this definition, the Solar System has five known dwarf planets: Ceres, Pluto, Haumea, Makemake, and Eris. Other objects may be classified in the future as dwarf planets, such as Sedna, Orcus, and Quaoar. Dwarf planets that orbit in the trans-Neptunian region are called "plutoids". The remainder of the objects in orbit around the Sun is small Solar System bodies.

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Figure 2.3 Planets and dwarf planets of the Solar System. Sizes are to scale, but relative distances from the Sun are not.

Planetary scientists use the terms gas, ice, and rock to describe the various classes of substances found throughout the Solar System. Rock is used to describe compounds with high condensation temperatures or melting points that remained solid under almost all conditions in the protoplanetary nebula. Rocky substances typically include silicates and metals such as iron and nickel. They are prevalent in the inner Solar System, forming most of the terrestrial planets and asteroids. Gases are materials with extremely low melting points and high vapor pressure such as molecular hydrogen, helium, and neon, which were always in the gaseous phase in the nebula. They dominate the middle region of the Solar System, comprising most of Jupiter and Saturn. Ices, like water, methane, ammonia, hydrogen sulfide and carbon dioxide, have melting points up to a few hundred Kelvin, while their phase depends on the ambient pressure and temperature. They can be found as ices, liquids, or gases in various places in the Solar System, while in the nebula they were either in the solid or gaseous phase. Icy substances comprise the majority of the satellites of the giant planets, as well as most of Uranus and Neptune (the so-called "ice giants") and the numerous small objects that lie beyond Neptune's orbit. Together, gases and ices are referred to as volatiles. 2.5 Solar Winds

The solar wind is actually an extension of the solar corona (outer atmosphere of the sun) in the form of more or less continuous outflow of ions and electrons. This is due to high temperature and more importantly small temperature gradient with height. As a result the solar corona is not at the hydrostatic equilibrium but is continuously by expanding into interplanetary space. The resulting outflow of coronal plasma is known as solar wind. Because of very high electrical conductivity of coronal plasma the magnetic field in the corona controls both the heat conduction and the outflow of the material. In the regions where the magnetic field lines reach high into corona the coronal expansion is greatly enhanced. The expansion speed is very low in the inner corona but increases rapidly with height. At the critical radius the thermal energy and the expansion

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kinetic energy become comparable; at this point the velocity is close to the velocity of sound in the plasma and the critical point is sometimes refer to as sonic point. At large distances the expansion velocity increases still further and solar wind becomes supersonic.The magnetic field is now carried along with the expanding plasma resulting in interplanetary magnetic fields. At about 20 R (radius of the sun) from the sun, the coronal expansion becomes very nearly radial but the rotation of the solar winds the interplanetary magnetic field lines into Archimedes spirals on the cones described by rotating radius vector Figure 2.4.

In early work on solar wind theory, incorrect assumptions about the electric field produced by the coronal plasma called Rannekock-Rossel and electric field derived under the assumption of static equilibrium led to evaporative models of the coronal expansion predicting much lower (subsonic) velocities that is solar breeze rather than solar winds. In situ measurements by space crafts have confirmed the basic velocity of the solar wind as measured near the earth are give in Table 2.2 The observations indicate the essentially continuous presence of magnetic field fluctuations in the solar wind plasma that seems to be predominantly Alfvěn waves being convected outward from the sun. In addition to being convected the waves move s outward from the sun with respect to plasma. Because of overall propagation it is presumed that the waves are originated near the sun-at least inside the critical radius. It has been suggested that photospheric supergranulation is the source of these waves.

Solar wind magnetic field lines are convected away from the sun by expanding solar wind. This interplanetary magnetic field is originated and ordered on large scale Observations made near the equatorial plane of the sun suggest that the magnetic field is originated into a few (typically four) sectors or regions where the magnetic field is predominantly directed either away from the sun or towards the sun along the basic Archimedes spiral induced by solar rotation as shown in Figure 2.4.

Property Medium Average MaximumFlux (108 ions cm-2 s-2) 1.0 3.0 100Velocity (km s-1) 200 400 900Density (ions cm-3) .4 6.5 100

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Electron Temperature (1000 K)

5 200 1000

Proton Temperature (1000 K)

3 50 1000

Magnetic Field Strength ( 10-5 = ץ G)

0.2 6.0 80

Alfvěn speed (km –s) 30 60 150Helium abundance (fraction per number)

0.0 0.05 0.25

Table 2.2 Properties of Solar Winds

Figure 2.4 Schematic diagram of the wrapped current sheet in the inner solar system (inside 6 AU). This current sheet divides the interplanetary magnetic field in the heliosphere into two regions with oppositely directed field lines. In one region the field polarity is towards the sun, in the other region it is away from the sun. The situation is shown for a four-sector structure. Formed by Archimedes spiral formed by solar rotation Full and dashed lines indicate the current sheet lying above and below the equatorial plane, respectively. The extend in latitude of the current sheet was assumed to be ±15º. The sun at the centre is not shown to scale.

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The solar wind extend into the regions around the sun approximately called the heliosphere and is expected to terminate at heliopause are at a distance R at which the pressure of the wind balance the pressure of interstellar space This interstellar pressure is due to a combination of contribution from galactic magnetic fields and, cosmic rays and interstellar gas. The value of R is not known but R ≈ 50 to 100 AU is often quoted.2.6 Energy Generation The rate at which the sun emits electromagnetic radiation into the space, and thus the rate at which energy must be generated within it, is about 4 x 1033 ergs/s .Further, the power output of the sun has been the same throughout the recorded history and according to geological evidences, not very different since the formation of the earth thousands of millions of years ago.It was suggested about 1928 that the energy source in the stars might be fusion of light elements into heavier elements. Since hydrogen and helium accounts for about 98 to 99 percent of the mass of most of the stars, we logically look first to these elements as probable reactants in any such fusion reaction. The helium atom s are about 4 times massive than that of hydrogen. Therefore it would take four atoms of hydrogen to produce one atom of helium. The masses of hydrogen and helium atoms are 1.007825U and 4.00268U, respectively. Let us compute the difference in the initial and the final masses.

4x 1.007825 = 4.03130U (mass of initial hydrogen atoms) - 4.00268U (mass of the helium atom) 0.02862U (mass loss in the transaction)

Here we include the mass of entire atoms not just the nuclei, because the electrons are involved as well, even though, in the stellar interiors, the hydrogen and helium are completely ionized. When hydrogen is converted into helium two positrons are created in the nuclear reactions, and these annihilate with two free electrons, adding to the energy produced.Thus with the mass lost by 0.02862U is 0.71 percent of the mass of the initial hydrogen. If 1 g of hydrogen turns into helium, 0.0071 g of material is converted into energy. The velocity of light is 3 x 1010 cm/s so the energy released is

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M = m.c2 = 0.0071 x (3x1010)2

= 6.4 x1018 ergs

This = 6 x1018 ergs is enough energy to raise the 5-m telescope150 Km above the ground. To produce the sun’s luminosity of 4 x 1033

ergs/s, some 600 million tons of hydrogen must be converted into helium per second with the simultaneous conversion of 4 million tons of matter into energy. As large as these numbers are the nuclear energy in the sun is still enormous. Suppose the half of the suns mass of 2x1033g is hydrogen that can be ultimately converted into helium, then the total store of nuclear energy in the sun would be 6 x 1052 ergs. Even at the sun’s current rate of expenditure the sun could survive more than 1010 years.

As a main sequence star the main source of energy of the sun is thermonuclear conversion of four protons to one helium atom with the release of the binding energy of 26.73 MeV. At the temperature less than ≈ 2.3 x 107K most of the energy is provided by proton –proton (PP) chain a series of reaction that yields 26.20 MeV in gamma rays and 0.53 MeV in neutrinos.

p (p, e+ +ע)de+ (e-)γ

d (p , γ)3He3He (3He, p+ p) 4He

At temperatures above 1.4 x 104 K alternative terminations involving the heavier species are more frequent; firstly

3He (4He, γ) 7Be

Then either 7Be (e-, ע) 7Li (pep reaction)

7Li (p, α) 4He Or 7Be (p, γ) 8B

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8B (e+ , +ע ) 8Be☼

8Be☼ 2 4He

This reaction produces neutrinos which should be detectable on the earth.At temperature above 1.7 x 107 K a very different reaction catalyzed by carbon, nitrogen and oxygen (hence CNO cycle) takes over. This is very sensitive to temperature (rate proportional to T17) whereas the p-p chain is only weakly dependent (rate proportional to T4). In solar model the CNO energy production is strongly concentrated at the core but even there it provides only 6% of the total energy production rate in the standard model. A lower core temperature, that would be consistent with the observed neutrino flux, would produce even less energy by the CNO cycle.

Summery

Nicolaus Copernicus was the first to develop a mathematically predictive heliocentric system.

The Solar System consists of the Sun and those celestial objects bound to it by gravity.

Solar System was formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago.

The four smaller inner planets, Mercury, Venus, Earth and Mars, also called the terrestrial planets they are primarily composed of rock and metal.

The four outer planets, Jupiter, Saturn, Uranus and Neptune, also called the gas giants, are composed largely of hydrogen and helium and are far more massive than the terrestrials.

Five individual objects, Ceres, Pluto, Haumea, Makemake and Eris, are recognized to be large enough to have been rounded by their own gravity, and are termed dwarf planets.

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Dwarf planets that orbit in the trans-Neptunian region are also called "plutoids".

The solar wind is actually an extension of the solar corona (outer atmosphere of the sun) in the form of more or less continuous outflow of ions and electrons.

It was suggested about 1928 that the energy source in the stars might be fusion of light elements into heavier elements.

Exercises

Fill in the blanks

1. Nicolaus Copernicus was the first to develop a mathematically predictive ________________.

2. Solar System was formed approximately ___________ billion years ago.

3. Asteroid belt lie between___________ and __________.

4. The _________ of Planets and _______ of dwarf planets are orbited by their moons.

5. The sun comprises approximately ___________ percent of the mass of the solar system.

6. The most popular theory of the formation of the solar system is ____________.

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7. The star derives their energy by ______________ conversion.

8. Asteroids never accreted to large planets due to their very low__________.

9. Most of the large objects in orbit round the sun lie near the orbit of the earth called ___________

10. The solar winds can be detected as far as ______AU.

Short questions with answerQ1. What is a solar system? When it is thought to be created?

Ans. The Solar System consists of the Sun and those celestial objects bound to it by gravity, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago.

Q2. What are the regions of solar system?

Ans. The Solar System is also home to two regions populated by smaller objects. The asteroid belt, which lies between Mars and Jupiter, is similar to the terrestrial planets as it is composed mainly of rock and metal. Beyond Neptune's orbit lie trans-Neptunian objects composed mostly of ices such as water, ammonia and methane. Within these regions, five individual objects, Ceres, Pluto, Haumea,  Makemake and Eris, are recognized to be large enough to have been rounded by their own gravity, and are thus termed dwarf planets.

Q3. Name the planets of solar system?

Ans. There are four smaller inner planets, Mercury, Venus, Earth  and Mars, also called the terrestrial planets they are primarily

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composed of rock and metal. The four outer planets, Jupiter, Saturn, Uranus and Neptune, also called the gas giants, are composed largely of hydrogen and helium and are far more massive than the terrestrials. Recently, five individual objects, Ceres, Pluto, Haumea,  Makemake and Eris, are recognized to be large enough to have been rounded by their own gravity, and are thus termed dwarf planets.

Q4. Do all planets and dwarf planets have natural satellites?

Ans. Six of the planets and three of the dwarf planets are orbited by natural satellites, usually termed "moons" after Earth's Moon. Each of the outer planets is encircled by planetary rings of dust and other particles.

Q5. What is the catastrophic theory of the origin of solar system?

Ans. The Catastrophic theory of origin of solar system suggest that a passing star pulled out the matter from the sun that later condensed into planets.

Q6 What is the nebular theory of the origin of solar system? When did it first appear?

Ans. It is generally accepted that the sun and planets formed together from the same original tenuous cloud of interstellar gas and dust called solar nebula. The idea appears to have been first suggested by the German philosopher Immanuel Kant, in mid 18th Century, and was developed into the specific model by French astronomer Marquis Pierre Simon de Laplace near the end of same century. This Kant- Laplace idea is known as nebular hypothesis. This Kant –Laplace model cannot be correct in detail, but the modern versions are consistent with well known laws of mechanics.

Q7. How often stars like the sun is formed?Ans. The study of stars has indicated that all stars are not formed in

the manner the sun was formed. Often, the original protostar fissions into two condensations to become a double star, and the original angular momentum are conserved in the orbital

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motions of two stars rather than in one star with the system of planets. Other times the cloud breaks up into cluster of stars.

Q8. How often planetary systems like that of sun is formed?Ans. We don’t know how often planetary systems are formed. At

most it’s only half the times, because about half the stars around us are member of binary star systems. Some recent studies have indicated that the formation of planetary systems might be relatively rare.

Q9. What is the heliosphere?Ans. We don’t know how often planetary systems are formed. At

most it’s only half the times, because about half the stars around us are member of binary star systems. Some recent studies have indicated that the formation of planetary systems might be relatively rare.

Q10. What amount of hydrogen must be converted into helium for the sun to sustain its present luminosity?

Ans. To produce the sun’s luminosity of 4 x 1033 ergs/s, some 600 million tons of hydrogen must be converted into helium per second with the simultaneous conversion of 4 million tons of matter into energy.

Study Questions

Q1. Give brief idea about the members of solar system.Q2. How solar system is thought to be originated? What are the two

important theories of its origin?Q3. On what grounds the catastrophic theory of the origin of solar

system is discarded?Q4. Explain the nebular theory of the origin of solar system.Q5. How do the planets formed?Q6. What is the theory of the formation of moons?Q7. Discuss the structure of solar system.Q8. What are solar winds? Q9. What is the major source of energy of the sun?Q10. Why do we not expect the nuclear fusion on the surface layer of

the star?

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Chapter 3

Sir Arthur Stanley

Eddington, OM, FRS

(28 December 1882 –

22 November 1944) was

a British astrophysicist

of the early 20th century.

The Eddington limit, the natural limit to the

luminosity of stars, or the radiation generated by

accretion onto a compact object, is named in his

honour

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The Sun and the Planets3.1 The Sun

The Sun is the Solar System's star, and far and away its chief component. Its large mass produces temperatures and densities in its core great enough to sustain nuclear fusion, which releases enormous amounts of energy, mostly radiated into space as electromagnetic radiation; peaking in the 400–to–700 nm band we call visible light.

The Sun is classified as a type G2 yellow dwarf, but this name is misleading as, compared to majority of stars in our galaxy, the Sun is rather large and bright. Stars are classified by the Hertzsprung-Russell diagram - a graph which plots the brightness of stars against their surface temperatures. Generally, hotter stars are brighter. Stars following this pattern are said to be on the main sequence, and the Sun lies right in the middle of it. However, stars brighter and hotter than the Sun are rare, while substantially dimmer and cooler stars, known as red dwarfs, are common, making up 85 percent of the stars in the galaxy. It is believed that the Sun's position on the main sequence puts it in the "prime of life" for a star, in that it has not yet exhausted its store of hydrogen for nuclear fusion. The Sun is growing brighter; early in its history it was 70 percent as bright as it is today.

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Figure 3.1 A transit of Venus, showing the size of the Sun in comparison to the planet

The Sun is a population I star; it was born in the later stages of the universe's evolution, and thus contains more elements heavier than hydrogen and helium ("metals" in astronomical parlance) than older population II stars. Elements heavier than hydrogen and helium were formed in the cores of ancient and exploding stars, so the first generation of stars had to die before the universe could be enriched with these atoms. The oldest stars contain few metals, while stars born later have more. This high metallicity is thought to have been crucial to the Sun's developing a planetary system, because planets are formed from accretion of "metals". These metals are heated to the gaseous state. The tremendous pressure is produced by the great weight of the sun’s layers. The high temperature of its interior and consequent thermonuclear reactions keeps the entire sun gaseous. There is no distinct surface we observe optically only the level in the sun at which the gases become opaque and prevent us from seeing deep into its interior. The temperature of that region is about 6000˚ K. Relatively, sparse outer gases extends for millions of kilometers into space in all directions. The visible part of the sun is 1,390.000 Km across. This is 109 times the diameter of the earth. Its volume is 1⅛ million times that of the earth. Its mass is 2 x 1033 g exceeds that of the earth by 333,000 times. The suns energy output is 5 x 1023 hp that provides all the light and heat for rest of the solar system. Some solar data obtained by various techniques are described in Table 3.1

Datum How Found Value

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Mean distance

Maximum distance from earth

Minimum distance from earth

Mass

Mean angular diameter

Diameter of photosphere

Mean Density

Gravitational acceleration at

photosphere(surface gravity)

Solar Constant

Luminosity

Spectral Class

Radar reflection from planets

Acceleration of earth

Direct Measurement

Angular size and distance

Mass/volume

GM/R2

Measured by instruments such

as bolometer

Solar Constant times area of

the spherical surface 1 AU in

radius

Spectrum

1 AU

149,597892 km

1.521 X 108 km

1.471 X 108 km

333,400 earth mass

1.99 X 1033g

31’59’’.3

109.3 times earths

diameter

1.39 x 10 cm

1.41g/cm3

27.9 times earths

surface gravity.

1.96 cal/min/cm2

1.368 x 106 ergs/s/cm2

3.8 x 1033 ergs/s

G2V

Table 3.1 Solar Data

3.2 Interplanetary medium

There are two main components of interplanetary medium namely interplanetary dust and interplanetary gas. The interplanetary dust can be considered as sparse distribution of micro meteorites throughout the solar system, or at least throughout the main disk that contains the orbits of the planets. These individual particles have been detected as they strike the spacecrafts. Further, these particles can be observed by the sunlight they reflect. On a dark clear night a faint band of light can be seen circling along the ecliptic which is

64

brightest near the sun and can be seen in the west within a few hours after the sunset or in the east within few hours before the sunrise. Sometimes, it can be seen as the complete band confined to ecliptic or zodiac, it is called as Zodiacal light. Spectrographic analysis of the zodiacal light seems to be sunlight, presumably reflected from microscopic solid particles. The stream of particles spreads outwards at roughly 1.5 million kilometers per hour, creating a tenuous atmosphere (the heliosphere) that permeates the Solar System out to at least 100 AU (see heliopause).  Apart from interplanetary dust it is thought that planetary atmosphere do not end abruptly but thins out gradually into interplanetary gas. The evidence to this effect is provided by space probes which reveal that interplanetary gas consists of ions and electrons ejected into space from the sun as solar wind. Geomagnetic storms on the Sun's surface, such as solar flares and coronal mass ejections, disturb the heliosphere, creating space weather. The largest structure within the heliosphere is the heliospheric current sheet, a spiral form created by the actions of the Sun's rotating magnetic field on the interplanetary medium. Thus we can say that interplanetary space contains minute widely spread particles and very sparse gas. In the neighborhood of earth there are only a few ions per cubic centimeter. This is a far better vacuum than can be produced in any terrestrial laboratory.

Earth's magnetic field stops its atmosphere from being stripped away by the solar wind. Venus and Mars do not have magnetic fields, and as a result, the solar wind causes their atmospheres to gradually bleed away into space. Coronal mass ejections and similar events blow magnetic field and huge quantities of material from the surface of the Sun. The interaction of this magnetic field and material with Earth's magnetic field funnels charged particles into the Earth's upper atmosphere, where its interactions create aurorae seen near the magnetic poles.

Cosmic rays originate outside the Solar System. The heliosphere partially shields the Solar System, and planetary magnetic fields (for those planets that have them) also provide some protection. The density of cosmic rays in the interstellar medium and the strength of

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the Sun's magnetic field change on very long timescales, so the level of cosmic radiation in the Solar System varies, though by how much is unknown.

The interplanetary medium is home to at least two disc-like regions of cosmic dust. The first, the zodiacal dust cloud, lies in the inner Solar System and causes zodiacal light. It was likely formed by collisions within the asteroid belt brought on by interactions with the planets. The second extends from about 10 AU to about 40 AU, and was probably created by similar collisions within the Kuiper belt.

3.3 PlanetsMost of the material of the solar system that is not a part of the sun itself is concentrated in the planets. In contrast to the sun the planets are small, relatively cool and solid or liquid. They are not self illuminating at visible wavelengths and shines with the reflected light of the sun As far as the nomenclature of the planets are concerned Two planets near the sun than the earth (mercury and Venus) are called inferior planets., while the ones with the orbit outside the earth’s are called superior planets. Four innermost planets Mercury through Mars are called inner planets. Jupiter, Saturn Neptune, Uranus are called outer planets. Finally, the four largest planets Jupiter, Saturn Neptune, Uranus are called jovian planets after Jupiter or occasionally major planets and other planets the terrestrial planets. The masses of the planets in terms of earths mass varies in the range from 0.055 (Mercury) to 318 (Jupiter). The mass of the Jupiter is greater than that of all other planets combined together. In diameter the planets range from 4878 Km (Mercury) to 143,000 Km (Jupiter). Most but not all the planets are surrounded by the gaseous atmospheres. All but two of the planets have natural satellites. Jupiter and Saturn leads with at least 64 known moons each with new ones keep turning up in our exploration to those worlds with interplanetary probes.

All the planets revolve about the sun in same direction from west to east. Their mean distance from the sun ranges from 0.39 AU (58 million kilometer) for mercury to 30.06 AU (Neptune).Their period of orbital revolution range from 88 days for Mercury to163 years for Neptune. The corresponding mean orbital velocities range from 48 Km/s to 5.4Km/s. the orbits of all planets are nearly in the same

66

plane, except Mercury whose orbit is inclined to that of earth by 7˚. The orbits of the planets are nearly circular; and have eccentricities less than 0.0 except mercury whose eccentricity is 0.21. All the planets rotate as they revolve about the sun. Rotation is the turning of an object on an axis running through it. As distinguished from the revolution, which is the motion of the object as a whole about another object or a point, Jovian planets are rapid rotators. Jupiter rotates rapidly in the period of 9h50m mercury 1½ times during its 88 days of revolution about the sun. Venus rotates still more slowly in 243 days but from east to west. Reverse to the rotation of most of the planets (that is retrograde). Some of the planets show marked oblateness or flattening due to their rapid rotation. Some of the orbital and Physical

Data of the planets are indicated in the Tables 3.2 and Table 3.3

Planet Semi majorAxis(AU)

OrbitalPeriod

(yr)

OrbitalSpeed(km/s)

OrbitalEccentricity

(e)

Inclinationof Orbit

to Ecliptic(°)

RotationPeriod(days)

Inclinationof Equator 

to Orbit(°)

Mercury 0.3871 0.2408 47.9 0.206 7.00 58.65 0

Venus 0.7233 0.6152 35.0 0.007 3.39 -243.01* 177.3

Earth 1.000 1 29.8 0.017 0.00 0.997 23.4

Mars 1.5273 1.8809 24.1 0.093 1.85 1.026 25.2

Jupiter 5.2028 11.862 13.1 0.048 1.31 0.410 3.1

Saturn 9.5388 29.458 9.6 0.056 2.49 0.426 26.7

Uranus 19.1914 84.01 6.8 0.046 0.77 -0.746* 97.9

Neptune 30.0611 164.79 5.4 0.010 1.77 0.718 29.6

Dwarf Planets

Ceres 2.76596 4.599 17.882 0.07976 10.587 0.378 ~3

Pluto 39.5294 248.54 4.7 0.248 17.15 -6.4* 122.5

Haumea 43.335 285.4 4.484 0.18874 28.19 0.163 ?

Makemake 45.791 309.88 4.419 0.159 28.96 ? ?

Eris 67.6681 557 3.436 0.44177 44.187 > 8 hrs? ?

Tables 3.2 Orbital Data of planets Negative values of rotation period indicate that the planet rotates in the direction opposite to that in which it orbits the Sun. This is called retrograde rotation.

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Inner Solar System

The inner Solar System is the traditional name for the region comprising the terrestrial planets and asteroids. Composed mainly of silicates and metals, the objects of the inner Solar System are relatively close to the Sun; the radius of this entire region is shorter than the distance between Jupiter and Saturn.

Figure 3.2 The inner planets. From left to right:  Mercury, Venus, Earth, and Mars (sizes to scale, interplanetary distances not)

Planet EquatorialRadius

(km)

MeanRadius (km)

Mass k(x

1024g)

BulkDensit

y(g cm-

3)

SiderealRotation Period

(d)

SiderealOrbit

Period (y)

V(1,0) (mag)

GeometricAlbedo

EquatorialGravity(m s-2)

Escape

Velocity

(km s-1)Mercury

2439.7±1.0

2439.7±1.0

0.330104±000036

5.427±007

58.6462 0.2406\8467

-0.60±0.10

0.106 3.70 4.25

Venus 6051.8±1.0

6051.8±1.0

4.86732±00049

5.243±003

-243.018 0.61519726

-4.47±0.07

0.65 8.87 10.36

Earth 6378.14±01

6371.00±01

5,97219±00060

5.5134±0006

0.99726968

1.0000174

-3.86 0.367 9.80 11.19

Mars 3396.19±1 3389.50±2

0.641693±000064

3.9340±0008

1.02595676

1.8808476

-1.52 0.150 3.71 5.03

Jupiter 71492±4 69911±6

1898.13±19

1.3262±0004

0.41354 11.862615

-9.40 0.52 24.79 60.20

Saturn 60268±4 58232±6

568.319±057

0.6871±0002

0.44401 29.447498

-8.88 0.47 10.44 36.09

Uranus 2559±4 25362±7

86.8103±0087

1.270±001

-0.71833 84.016846

-7.15 0.51 8.87 21.38

Neptune

24765±15 24622±19

102.410±010

1.638±004

0.67125 164,79123

-6.87 0.41 11.15 23.56

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Pluto 1151±6 1151±6

.01309±00018

2.05±04

-6.3872 247.92065

-1.0 0.3 0.66 1.23

Table 3.3 Physical Data of planets and Pluto

The four inner or terrestrial planets have dense, rocky compositions, few or no moons, and no ring systems. They are composed largely of refractory minerals, such as the silicates which form their crusts and mantles, and metals such as iron and nickel, which form their cores. Three of the four inner planets (Venus, Earth and Mars) have atmospheres substantial enough to generate weather; all have impact craters and tectonic surface features such as rift valleys and volcanoes. The term inner planet should not be confused with inferior planet, which designates those planets which are closer to the Sun than Earth is (i.e. Mercury and Venus).

1. MercuryMercury (0.4 AU from the Sun) is the closest planet to the Sun and the smallest planet (0.055 Earth masses). Mercury has no natural satellites, and it’s only known geological features besides impact craters are lobed ridges or rupes, probably produced by a period of contraction early in its history. Mercury's almost negligible atmosphere consists of atoms blasted off its surface by the solar wind. Its relatively large iron core and thin mantle have not yet been adequately explained. Hypotheses include that its outer layers were stripped off by a giant impact, and that it was prevented from fully accreting by the young Sun's energy.

2. VenusVenus (0.7 AU) is close in size to Earth, (0.815 Earth masses) and like Earth, has a thick silicate mantle around an iron core, a substantial atmosphere and evidence of internal geological activity. However, it is much drier than Earth and its atmosphere is ninety times as dense. Venus has no natural satellites. It is the hottest planet, with surface temperatures over 400 °C, most likely due to the amount of greenhouse gases in the

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atmosphere. No definitive evidence of current geological activity has been detected on Venus, but it has no magnetic field that would prevent depletion of its substantial atmosphere, which suggests that its atmosphere is regularly replenished by volcanic eruptions.

3. EarthEarth (1 AU) is the largest and densest of the inner planets, the only one known to have current geological activity, and is the only place in the universe where life is known to exist. Its liquid hydrosphere is unique among the terrestrial planets, and it is also the only planet where plate tectonics has been observed. Earth's atmosphere is radically different from those of the other planets, having been altered by the presence of life to contain 21% free oxygen. It has one natural satellite, the Moon, the only large satellite of a terrestrial planet in the Solar System.

4. MarsMars (1.5 AU) is smaller than Earth and Venus (0.107 Earth masses). It possesses an atmosphere of mostly carbon dioxide with a surface pressure of 6.1 millibars (roughly 0.6 percent that of the Earth's). Its surface, peppered with vast volcanoes such as Olympus Mons and rift valleys such as Valles Marineris, shows geological activity that may have persisted until as recently as 2 million years ago. Its red color comes from iron oxide (rust) in its soil. Mars has two tiny natural satellites (Deimos and Phobos) thought to be captured asteroids.

3.5 Asteroid belt

Asteroids are mostly small Solar System bodies composed mainly of refractory rocky and metallic minerals. The main asteroid belt occupies the orbit between Mars and Jupiter, between 2.3 and 3.3 AU from the Sun. It is thought to be remnants from the Solar System's formation that failed to coalesce because of the

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gravitational interference of Jupiter. Asteroids range in size from hundreds of kilometers across to microscopic. All asteroids save the largest, Ceres, are classified as small Solar System bodies, but some asteroids such as Vesta and Hygieia may be reclassed as dwarf planets if they are shown to have achieved hydrostatic equilibrium.

The asteroid belt contains tens of thousands, possibly millions, of objects over one kilometer in diameter. Despite this, the total mass of the main belt is unlikely to be more than a thousandth of that of the Earth. The main belt is very sparsely populated; spacecraft routinely pass through without incident. Asteroids with diameters between 10 and 10−4 m are called meteoroids.

Figure 3.3 Image of the main asteroid belt and the Trojan asteroids

3.6 CeresCeres (2.77 AU) is the largest body in the asteroid belt and is classified as a dwarf planet. It has a diameter of slightly less than 1000 km, and a mass large enough for its own gravity to pull it into a spherical shape. Ceres was considered a planet when it was discovered in the 19th century, but was reclassified as an asteroid in the 1850s as further observation revealed additional asteroids. It was again reclassified in 2006 as a dwarf planet.

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3.7 Asteroid groups

Asteroids in the main belt are divided into asteroid groups and families based on their orbital characteristics. Asteroid moons are asteroids that orbit larger asteroids. They are not as clearly distinguished as planetary moons, sometimes being almost as large as their partners. The asteroid belt also contains main-belt comets which may have been the source of Earth's water.

Trojan asteroids are located in either of Jupiter's L4 or L5 points (gravitationally stable regions leading and trailing a planet in its orbit); the term "Trojan" is also used for small bodies in any other planetary or satellite Lagrange point. Hilda asteroids are in a 2:3 resonance with Jupiter; that is, they go around the Sun three times for every two Jupiter orbits. The inner Solar System is also dusted with rogue asteroids, many of which cross the orbits of the inner planets.

3.8 Outer Solar System

The outer region of the Solar System is home to the gas giants and their large moons. Many short period comets, including the centaurs, also orbit in this region. Due to their greater distance from the Sun, the solid objects in the outer Solar System are composed of a higher proportion of ices (such as water, ammonia, methane, often called ices in planetary science) than the rocky denizens of the inner Solar System, as the colder temperatures allow these compounds to remain solid.

3.9 Outer Planets

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Figure 3.4 From top to bottom:  Neptune, Uranus, Saturn, and Jupiter (not to scale)

The four outer planets, or gas giants (sometimes called Jovian planets), collectively make up 99 percent of the mass known to orbit the Sun. Jupiter and Saturn consist overwhelmingly of hydrogen and helium; Uranus and Neptune possess a greater proportion of ices in their makeup. Some astronomers suggest they belong in their own category, “ice giants.”[ All four gas giants have rings, although only Saturn's ring system is easily observed from Earth. The term outer planet should not be confused with superior planet, which designates planets outside Earth's orbit and thus includes both the outer planets and Mars.

1. JupiterJupiter (5.2 AU), at 318 Earth masses, is 2.5 times all the mass of all the other planets put together. It is composed largely of hydrogen and helium. Jupiter's strong internal heat creates a number of semi-permanent features in its atmosphere, such as cloud bands and the Great Red Spot. Jupiter has 63 known satellites. The four largest, Ganymede, Callisto, Io, and Europa, show similarities to the terrestrial planets, such as volcanism and internal heating. Ganymede, the largest satellite in the Solar System, is larger than Mercury.

2. Saturn

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Saturn (9.5 AU), distinguished by its extensive ring system, has several similarities to Jupiter, such as its atmospheric composition and magnetosphere. Although Saturn has 60% of Jupiter's volume, it is less than a third as massive, at 95 Earth masses, making it the least dense planet in the Solar System. Saturn has 60 confirmed satellites; two of which, Titan and Escalades, show signs of geological activity, though they are largely made of ice. Titan is larger than Mercury and the only satellite in the Solar System with a substantial atmosphere.

3. UranusUranus (19.6 AU), at 14 Earth masses, is the lightest of the outer planets. Uniquely among the planets, it orbits the Sun on its side; its axial tilt is over ninety degrees to the ecliptic. It has a much colder core than the other gas giants, and radiates very little heat into space. Uranus has 27 known satellites, the largest ones being Titania, Oberon, Umbriel, Ariel and Miranda.

4. NeptuneNeptune (30 AU), though slightly smaller than Uranus, is more massive (equivalent to 17 Earths) and therefore more dense. It radiates more internal heat, but not as much as Jupiter or Saturn. Neptune has 13 known satellites. The largest, Triton, is geologically active, with geysers of liquid nitrogen. Triton is the only large satellite with a retrograde orbit. Neptune is accompanied in its orbit by a number of minor planets, termed Neptune Trojans that are in 1:1 resonance with it.

3.10 Comets

Comets are small Solar System bodies, typically only a few kilometers across, composed largely of volatile ices. They have highly eccentric orbits, generally a perihelion within the orbits of the inner planets and an aphelion far beyond Pluto. When a comet enters the inner Solar System, its proximity to the Sun causes its icy surface

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to sublimate and ionize, creating a coma: a long tail of gas and dust often visible to the naked eye.

Figure 3. 5 Comet Hale-Bopp

Short-period comets have orbits lasting less than two hundred years. Long-period comets have orbits lasting thousands of years. Short-period comets are believed to originate in the Kuiper belt, while long-period comets, such as Hale-Bopp, are believed to originate in the Oort cloud. Many comet groups, such as the Kreutz Sungrazers, formed from the breakup of a single parent. Some comets with hyperbolic orbits may originate outside the Solar System, but determining their precise orbits is difficult. Old comets that have had most of their volatiles driven out by solar warming are often categorized as asteroids.

3.11 Centaurs

The centaurs are icy comet-like bodies with a semi-major axis greater than Jupiter (5.5 AU) and less than Neptune (30 AU). The largest known centaur, 10199 Chariklo, has a diameter of about 250 km. The first centaur discovered, 2060 Chiron, has also been classified as comet (95P) since it develops a coma just as comets do when they approach the Sun.

3.12 Trans-Neptunian region

The area beyond Neptune, or the "trans-Neptunian region", is still largely unexplored. It appears to consist overwhelmingly of small worlds (the largest having a diameter only a fifth that of the Earth and a mass far smaller than that of the Moon) composed mainly of rock

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and ice. This region is sometimes known as the "outer Solar System", though others use that term to mean the region beyond the asteroid belt.

3.13 Kuiper belt

The Kuiper belt, the region's first formation, is a great ring of debris similar to the asteroid belt, but composed mainly of ice. It extends between 30 and 50 AU from the Sun. It is composed mainly of small Solar System bodies, but many of the largest Kuiper belt objects, such as Quaoar, Varuna, and Orcus, may be reclassified as dwarf planets. There are estimated to be over 100,000 Kuiper belt objects with a diameter greater than 50 km, but the total mass of the Kuiper belt is thought to be only a tenth or even a hundredth the mass of the Earth. Many Kuiper belt objects have multiple satellites, and most have orbits that take them outside the plane of the ecliptic.

Figure 3.6 Plot of all known Kuiper belt objects, set against the four outer planets

The Kuiper belt can be roughly divided into the "classical" belt and the resonances. Resonances are orbits linked to that of Neptune (e.g. twice for every three Neptune orbits, or once for every two). The first resonance actually begins within the orbit of Neptune itself. The classical belt consists of objects having no resonance with Neptune, and extends from roughly 39.4 AU to 47.7 AU. Members of the classical Kuiper belt are classified as cubewanos, after the first of

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their kind to be discovered, (15760) 1992 QB1, and are still in near primordial, low-eccentricity orbits.

3.14 Pluto and CharonPluto (39 AU average), a dwarf planet, is the largest known object in the Kuiper belt. When discovered in 1930, it was considered to be the ninth planet; this changed in 2006 with the adoption of a formal definition of planet. Pluto has a relatively eccentric orbit inclined 17 degrees to the ecliptic plane and ranging from 29.7 AU from the Sun at perihelion (within the orbit of Neptune) to 49.5 AU at aphelion. It is unclear whether Charon, Pluto's largest moon, will continue to be classified as such or as a dwarf planet itself. Both Pluto and Charon orbit a barycenter of gravity above their surfaces, making Pluto-Charon a binary system. Two much smaller moons, Nix and Hydra, orbit Pluto and Charon. Pluto has a 3:2 resonance with Neptune, meaning that Pluto orbits twice round the Sun for every three Neptunian orbits. Kuiper belt objects whose orbits share this resonance are called plutinos.

3.15 Haumea and MakemakeHaumea (43.34 AU average), and Makemake (45.79 AU average), while smaller than Pluto, are the largest known objects in the classical Kuiper belt (that is, they are not in a confirmed resonance with Neptune). Haumea is an egg-shaped object with two moons. Makemake is the brightest object in the Kuiper belt after Pluto. Originally designated 2003 EL61 and 2005 FY9 respectively, they were given names and designated dwarf planets in 2008. Their orbits are far more inclined than Pluto's, at 28° and 29°.

3.16 Scattered disc

The scattered disc, which overlaps the Kuiper belt but extends much further outwards, is thought to be the source of short-period comets. Scattered disc objects are believed to have been ejected into erratic orbits by the gravitational influence of Neptune's early outward

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migration. Most scattered disc objects (SDOs) have perihelia within the Kuiper belt but aphelia as far as 150 AU from the Sun. SDOs' orbits are also highly inclined to the ecliptic plane, and are often almost perpendicular to it. Some astronomers consider the scattered disc to be merely another region of the Kuiper belt, and describe scattered disc objects as "scattered Kuiper belt objects." Some astronomers also classify centaurs as inward-scattered Kuiper belt objects along with the outward-scattered residents of the scattered disc.

3.17 ErisEris (68 AU average) is the largest known scattered disc object, and caused a debate about what constitutes a planet, since it is at least 5% larger than Pluto with an estimated diameter of 2400 km (1500 mi). It is the largest of the known dwarf planets. It has one moon, Dysnomia. Like Pluto, its orbit is highly eccentric, with a perihelion of 38.2 AU (roughly Pluto's distance from the Sun) and an aphelion of 97.6 AU, and steeply inclined to the ecliptic plane.

3.18 Farthest regions

The point at which the Solar System ends and interstellar space begins is not precisely defined, since its outer boundaries are shaped by two separate forces: the solar wind and the Sun's gravity. The outer limit of the solar wind's influence is roughly four times Pluto's distance from the Sun; this heliopause is considered the beginning of the interstellar medium. However, the Sun's Roche sphere, the effective range of its gravitational influence, is believed to extend up to a thousand times farther.

3.19 Heliopause

The heliosphere is divided into two separate regions. The solar wind travels at roughly 400 km/s until it collides with the interstellar wind; the flow of plasma in the interstellar medium. The collision occurs at the termination shock, which is roughly 80–100 AU from the Sun upwind of the interstellar medium and roughly 200 AU from the Sun

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downwind. Here the wind slows dramatically, condenses and becomes more turbulent, forming a great oval structure known as the heliosheath that looks and behaves very much like a comet's tail, extending outward for a further 40 AU on the upwind side but tailing many times that distance downwind. Both Voyager 1 and Voyager 2 are reported to have passed the termination shock and entered the heliosheath, at 94 and 84 AU from the Sun, respectively. The outer boundary of the heliosphere, the heliopause, it is the point at which the solar wind finally terminates and is the beginning of interstellar space.

Figure 3.7 The Voyagers entering the heliosheath

The shape and form of the outer edge of the heliosphere is likely affected by the fluid dynamics of interactions with the interstellar medium as well as solar magnetic fields prevailing to the south, e.g. it is bluntly shaped with the northern hemisphere extending 9 AU (roughly 900 million miles) farther than the southern hemisphere. Beyond the heliopause, at around 230 AU, lies the bow shock, a plasma "wake" left by the Sun as it travels through the Milky Way.

Figure 3.8 The Hubble Space Telescope imaged this view in February 1995. The arcing, graceful structure is actually a bow

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shock about half a light-year across, created from the wind from the star L.L. Orionis colliding with the Orion Nebula flow.

NASA's Voyager spacecrafts the Voyager 1 and 2, nearly 15 years after they left home have discovered the first direct evidence of the long- sought-after heliopause -- the boundary that separates Earth's solar system from interstellar space at the distance of 84 AU. Voyager 1 crosses Termination Shock on December 18, 2004 and Voyager 2 crosses Termination Shock on September 5 2007 and has been transmitting valuable data on radiation levels and solar wind back to the Earth, Since passage through the termination shock, the spacecraft has been operating in the heliosheath environment which is still dominated by the Sun's magnetic field and particles contained in the solar wind. The heliosheath exploration phase ends with passage through the heliopause which is the outer extent of the Sun's magnetic field and solar wind. The thickness of the heliosheath is uncertain and could be tens of AU thick taking several years to traverse. Passage through the heliopause begins the interstellar exploration phase with the spacecraft operating in an interstellar wind dominated environment. As per Voyager radio data combined with the plasma measurements taken at the spacecraft that give us a better guess about where the heliopause is. Based on the solar wind speed, the time that has elapsed since the mid-1992 solar event and the strength of the radio emissions, our best guess for the upper limit of the heliopause currently is about 90 to 120 astronomical units (AU) from the sun.

Voyager 1 is escaping the solar system at a speed of about 3.6 AU per year, 35 degrees out of the ecliptic plane to the north, in the general direction of the Solar Apex (the direction of the Sun's motion relative to nearby stars). Voyager 2 is also escaping the solar system at a speed of about 3.3 AU per year, 48 degrees out of the ecliptic plane to the south.

The Voyagers should cross the heliopause 10 to 20 years after reaching the termination shock. The Voyagers have enough electrical power and thruster fuel to operate at least until 2020. By that time, Voyager 1 will be 12.4 billion miles (19.9 billion KM) from the Sun and Voyager 2 will be 10.5 billion miles (16.9 billion KM) away. Eventually, the Voyagers will pass other stars. In about 40,000 years, Voyager 1

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will drift within 1.6 light years (9.3 trillion miles) of AC+79 3888, a star in the constellation of Camelopardalis. In some 296,000 years, Voyager 2 will pass 4.3 light years (25 trillion miles) from Sirius, the brightest star in the sky. The Voyagers are destined—perhaps eternally—to wander the Milky Way. As of February 2010, Voyager 1 was at a distance of 16.9 Billion Kilometers (112.7 AU) from the sun and Voyager 2 at a distance of 13.7 Billion kilometers (91.5 AU).

Figure 3.9 Trajetories of voyager 1 and 2 during their interstellar mission

3.20 Oort cloud

The hypothetical Oort cloud is a spherical cloud of up to a trillion icy objects that is believed to be the source for all long-period comets and to surround the Solar System at roughly 50,000 AU (around 1 light-year (LY)), and possibly to as far as 100,000 AU (1.87 LY). It is believed to be composed of comets which were ejected from the inner Solar System by gravitational interactions with the outer planets. Oort cloud objects move very slowly, and can be perturbed by infrequent events such as collisions, the gravitational effects of a passing star, or the galactic tide, the tidal force exerted by the Milky Way.

3.21 Sedna

90377 Sedna (525.86 AU average) is a large, reddish Pluto-like object with a gigantic, highly elliptical orbit that takes it from about 76 AU at perihelion to 928 AU at aphelion and takes 12,050 years to complete. Mike Brown, who discovered the object in 2003, asserts

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that it cannot be part of the scattered disc or the Kuiper belt as its perihelion is too distant to have been affected by Neptune's migration. He and other astronomers consider it to be the first in an entirely new population, which also may include the object 2000 which has a perihelion of 45 AU, an aphelion of 415 AU, and an orbital period of 3,420 years. Brown terms this population the "Inner Oort cloud”. As it may have formed through a similar process, although it is far closer to the Sun. Sedna is very likely a dwarf planet, though its shape has yet to be determined with certainty.

3.22 Satellites The Satellites of the planets are the next prominent members of the solar system.

1. Natural satellite

A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called the primary. Technically, the term natural satellite could refer to a planet orbiting a star, or a dwarf galaxy orbiting a major galaxy, but it is normally synonymous with moon and used to identify non-artificial satellites of planets, dwarf planets, and minor planets.

As of September 2008, 335 bodies are formally classified as moons. They include 167 orbiting six of the eight planets, 6 orbiting three of the five dwarf planets, 104 asteroid moons, and 58 satellites of Trans-Neptunian objects, some of which will likely turn out to be dwarf planets. Some 150 additional small bodies were observed within Saturn's ring system, but they were not tracked long enough to establish orbits. Planets around other stars are likely to have natural satellites as well, although none have been observed.

The large gas giants have extensive systems of moons, including half a dozen comparable in size to Earth's moon: the four Galilean moons, Saturn's Titan, and Neptune's Triton. Saturn has an additional six mid-sized moons massive enough to have achieved hydrostatic equilibrium, and Uranus has five. Of the inner planets, Mercury and Venus have no moons at all; Earth has one

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large moon, known as the Moon; and Mars has two tiny moons,  Phobos  and  Deimos. It has been suggested that a few moons, notably Europe, one of Jupiter's Galilean moons, may harbor life, though there is currently no direct evidence to support this claim.

Among the dwarf planets, Ceres has no moons (though many objects in the asteroid belt do). Pluto has three known satellites, the rather large Charon and the smaller Nix and Hydra.  Haumea has two moons, and Eris has one. The Pluto-Charon system is unusual in that the center of mass lies in open space between the two, a characteristic of a double planet system. The natural satellites orbiting relatively close to the planet on prograde orbits (regular satellites) are generally believed to have been formed out of the same collapsing region of the protoplanetary disk that gave rise to its primary. In contrast, irregular satellites (generally orbiting on distant, inclined, eccentric and/or retrograde orbits) are thought to be captured asteroids possibly further fragmented by collisions. The Earth's Moon and possibly Charon are exceptions among large bodies in that they are believed to have originated by the collision of two large proto-planetary objects (see the giant impact hypothesis). The material that would have been placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting moons. As opposed to planetary-sized bodies, asteroid moons are thought to commonly form by this process.

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Figure 3.8 Selected moons, with the Earth to scale. Nineteen moons are large enough to be round, and one, Titan, has a substantial atmosphere.

Triton is another exception, which although large and in a close, circular orbit, is thought to be a captured dwarf planet.

Geological activity on Moons

Of the nineteen known moons massive enough to have lapsed into hydrostatic equilibrium, several remain geologically active today. Io is the most volcanically active body in the Solar System, while Europa, Enceladus, Titan and Triton display evidence of ongoing tectonic activity and cryovolcanism. In the first three cases, the geological activity is powered by the tidal heating resulting from having eccentric orbits close to their gas giant primaries. (This mechanism would have also operated on Triton in the past, before its orbit was circularized.) Many other moons, such as Earth's Moon, Ganymede, Tethys and Miranda, show evidence of past geological activity, resulting from energy sources such as the decay of their primordial radioisotopes, greater past orbital eccentricities (due in some cases to past orbital resonances), or the differentiation or freezing of their interiors. Enceladus and Triton both have active features resembling geysers, although in the case of Triton solar heating appears to provide the energy. Titan and Triton have significant atmospheres; Titan also has methane lakes, and presumably rain. Four of the largest moons, Europa, Ganymede, Callisto, and Titan, are thought to have subsurface oceans of liquid water, while smaller Enceladus may have localized subsurface water.

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Figure 3.9 Two moons: Saturn's moon Dione occults Encel adusOrigin

2. Orbital characteristics

Satellite orbits are called regular or prograde if they are in the same direction as the planet's rotation otherwise they are called irregular or retrograde (The term irregular can also refer to the shape of a satellite). Most of the major moons in the solar system have regular orbits (Triton being the exception) while most of the small moons have irregular orbits

3. Tidal locking

The regular natural satellites in the solar system are tidally locked to their primaries, meaning that the same side of the moon always faces the planet. The only known exception is Saturn's moon Hyperion, which rotates chaotically because of the gravitational influence of Titan.

In contrast, the outer moons of the gas giants (irregular satellites) are too far away to have become locked. For example, Jupiter's moon Himalia, Saturn's moon Phoebe, and Neptune's moon Nereid have rotation period in the range of ten hours, while their orbital periods are hundreds of days.

4. Satellites of satellites

No moons of moons (natural satellites that orbit the natural satellite of another body) are known. In most cases, the tidal effects of the primary would make such a system unstable.

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Figure 3.10 Artist impression of Rhea's rings

However, calculations performed after the recent detection  of a possible ring system around Saturn's moon Rhea indicate that Rhean orbits would be stable. Furthermore, the suspected rings are thought to be narrow, a phenomenon normally associated with shepherd moons.

5. Trojan satellites

Two moons are known to have small companions at their L4 and L5 Lagrangian points, sixty degrees ahead and behind the body in its orbit. These companions are called Trojan moons, as their orbits are analogous to the Trojan asteroids of Jupiter. The Trojan moons are Telesto and Calypso, which are the leading and following companions respectively of Tethys; and Helene and Polydeuces, the leading and following companions of Dione.

6. Asteroid moon

The discovery of 243 Ida's moon Dactyl in the early 1990s confirmed that some asteroids have moons; indeed, 87 Sylvia has two. Some, such as 90 Antiope, are double asteroids with two comparably sized components.

The relative masses of the moons of the Solar system. Mimas, Enceladus, and Miranda are too small to be visible at this scale. All the irregularly shaped moons, even added together, would also be too small to be visible.The largest natural satellites in the Solar System (those bigger than about 3000 km across) are Earth's moon, Jupiter's Galilean moons (Io, Europa, Ganymede, and Callisto), Saturn’s moon Titan, and Neptune’s captured moon Triton. For smaller moons see the articles on the appropriate planet. In addition to the moons of the various planets there are also over 80 known moons of the dwarf planets, asteroids and other small solar system bodies. Some studies estimate that up to 15% of all trans-Neptunian objects could have satellites

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Figure 3.11 The relative masses of the moons of the Solar system

Table 3.4 present the comparative view of the natural satellites by classifying the moons of the solar system by diameter. The column on the right includes some notable planets, dwarf planets, asteroids, and Trans-Neptunian Objects for comparison. The moons of the planets are named after mythological figures. These are predominately Greek, except for the Uranian moons, which are named after Shakespearean characters. The nineteen bodies massive enough to have achieved hydrostatic equilibrium are in bold in the chart below and labeled on the chart at right, though a few of the smaller ones are not visible at the scale of the chart. Minor planets suspected but not proven to have achieved a hydrostatic equilibrium are also shown.

3.23 Terminology

The first known natural satellite was the Moon (Luna in Latin). Until the discovery of the Galilean satellites in 1610, however, there was no opportunity for referring to such objects as a class. Galileo chose

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Mean diameter(km)

Satellites of planets Dwarf planet satellites

Satellites ofSSSBs

Non-satellitesfor comparisonEarth Mars Jupiter Saturn Uranus Neptune Pluto

Haumea

Eris

6000-8000

Mars

4000-6000

GanymedeCallisto

Titan Mercury

3000-4000

The Moon

IoEuropa

2000-3000

TritonErisPluto

1500-2000

RheaTitaniaOberon

MakemakeHaumea

1000-1500

IapetusDioneTethys

UmbrielAriel

Charon

90377 Sedna90482 Orcus50000 Quaoar2007 OR10

500-1000

Enceladus

Ceres20000 Varuna28978 Ixion2 Pallas, 4 Vestamany more TNOs

250-500MimasHyperion

MirandaProteusNereid

Hiʻiaka

S/2005 (79360) 190482 Orcus I "Vanth"

10 Hygiea511 Davida704 Interamnia87 Sylviaand many others

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100-250AmaltheaHimaliaThebe

PhoebeJanusEpimetheus

SycoraxPuckPortia

LarissaGalateaDespina

NamakaDysnomia

65489 Ceto I Phorcys617 Patroclus I Menoetius24 more moons of TNO

3 Juno1992 QB15 Astraea42355 Typhonand many others

50-100ElaraPasiphaë

PrometheusPandora

CalibanJulietBelindaCressidaRosalindDesdemonaBianca

ThalassaHalimedeNesoNaiad

HydraNix

50000 Quaoar I Weywot90 Antiope I42355 Typhon I Echidna58534 Logos I Zoe5 more moons of TNOs

90 Antiope I58534 Logosand many others

25-50

CarmeMetisSinopeLysitheaAnanke

SiarnaqHeleneAlbiorixAtlasPan

OpheliaCordeliaSetebosProspero PerditaStephano

SaoLaomedeiaPsamathe

22 Kalliope I Linus

many

10-25

PhobosDeimos

LedaAdrastea

TelestoPaaliaqCalypsoYmirKiviuqTarvosIjiraq rriapus

MabCupidFranciscoFerdinandMargaretTrinculo

762 Pulcova I87 Sylvia I Romulus624 Hektor I(45) Eugenia I Petit-Prince121 Hermione I283 Emma I1313 Berna I107 Camilla I

433 Eros1313 Bernaand many others

less than 10

at least 47 at least 3587 Sylvia I Remus

many

Table 3.4 Size of the Satellites of the planets

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to refer to his discoveries as Planetæ ("planets"), but later discoverers chose other terms to distinguish them from the objects they orbited. Christiaan Huygens, the discoverer of Titan, was the first to use the term moon for such objects, calling Titan Luna Saturni or Luna Saturnia – "Saturn's moon" or "The Saturnian moon", because it stood in the same relation to Saturn as the Moon did to the Earth. The first to use of the term satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iovis sattelitibus erronibus ("Narration about Four Satellites of Jupiter Observed") in 1610. He derived the term from the Latin word satelles, meaning "guard", "attendant", or "companion", because the satellites accompanied their primary planet in their journey through the heavens. As additional moons of Saturn were discovered the term "moon" was abandoned. Giovanni Domenico Cassini sometimes referred to his discoveries as planets in French, but more often as satellites.

The term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of "moon". In 1957, however, the launching of the artificial object Sputnik created a need for new terminology. The terms man-made satellite or artificial moon were very quickly abandoned in favor of the simpler satellite, and as a consequence, the term has come to be linked primarily with artificial objects flown in space – including, sometimes, even those which are not in orbit around a planet.

As a consequence of this shift in meaning, the term moon, which had continued to be used in a generic sense in works of popular science and in fiction, has regained respectability and is now used interchangeably with satellite, even in scientific articles. When it is necessary to avoid both the ambiguity of confusion with the Earth's moon on the one hand, and artificial satellites on the other, the term natural satellite (using "natural" in a sense opposed to "artificial") is used.

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3.24 The definition of a moonThere is no established lower limit on what should be considered a moon. Every body with an identified orbit, some as small as a kilometer across, has been identified as a moon, though objects a tenth that size within Saturn's rings, which have not been directly observed, have been called moonlets. Small asteroid moons, such as Dactyl, have also been called moonlets. The upper limit is also vague. When the masses of two orbiting bodies are similar enough that one cannot be said to orbit the other, they are described as a double body rather than primary and satellite. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition as to what constitutes a moon. Some authors consider the Pluto-Charon system to be a double (dwarf) planet. The most common dividing line on what is considered a moon rests upon whether the barycenter is below the surface of the larger body, though this is somewhat arbitrary, as it relies on distance as well as relative mass.

Figure 3.12 Comparison of Earth and the Moon

Figure 3.13 Comparison of Jupiter's Great Red Spot and Jupiter's four largest moons. Compared to Earth/Luna and Pluto/Charon, there is a much greater difference in mass.

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3.25 Boundaries of Solar System

Much of our Solar System is still unknown. The Sun's gravitational field is estimated to dominate the gravitational forces of surrounding stars out to about two light years (125,000 AU). Lower estimates for the radius of the Oort cloud, by contrast, do not place it farther than 50,000 AU. Despite discoveries such as Sedna, the region between the Kuiper belt and the Oort cloud, an area tens of thousands of AU in radius, is still virtually unmapped. There are also ongoing studies of the region between Mercury and the Sun. Objects may yet be discovered in the Solar System's uncharted regions.

3.26 Location of the Solar System within our Galaxy

The Solar System is located in the Milky Way Galaxy, a barred spiral galaxy with a diameter of about 100,000 light-years containing about 200 billion stars. Our Sun resides in one of the Milky Way's outer spiral arms, known as the Orion Arm or Local Spur. The Sun lies between 25,000 and 28,000 light years from the Galactic Centre, and its speed within the galaxy is about 220 kilometers per second, so that it completes one revolution every 225–250 million years. This revolution is known as the Solar System's cosmic year. The solar apex, the direction of the Sun's path through interstellar space, is near the constellation of Hercules in the direction of the current location of the bright star Vega.

The Solar System's location in the galaxy is very likely a factor in the evolution of life on Earth. Its orbit is close to being circular and is at roughly the same speed as that of the spiral arms, which means it passes through them only rarely. Since spiral arms are home to a far larger concentration of potentially dangerous supernovae, this has given Earth long periods of interstellar stability for life to evolve. The Solar System also lies well outside the star-crowded environs of the galactic centre. Near the centre, gravitational tugs from nearby stars could perturb bodies in the Oort cloud and send many comets into the inner Solar System, producing collisions with potentially catastrophic implications for life on Earth. The intense radiation of the galactic

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centre could also interfere with the development of complex life. Even at the Solar System's current location, some scientists have hypothesized that recent supernovae may have adversely affected life in the last 35,000 years by flinging pieces of expelled stellar core towards the Sun in the form of radioactive dust grains and larger, comet-like bodies.

3.27 Neighborhood

The immediate galactic neighborhood of the Solar System is known as the Local Interstellar Cloud or Local Fluff, an area of dense cloud in an otherwise sparse region known as the Local Bubble, an hourglass-shaped cavity in the interstellar medium roughly 300 light years across. The bubble is suffused with high-temperature plasma that suggests it is the product of several recent supernovae.

There are relatively few stars within ten light years (95 trillion km) of the Sun. The closest is the triple star system Alpha Centauri, which is about 4.4 light years away. Alpha Centauri A and B are a closely tied pair of Sun-like stars, while the small red dwarf Alpha Centauri C (also known as Proxima Centauri) orbits the pair at a distance of 0.2 light years. The stars next closest to the Sun are the red dwarfs Barnard's Star (at 5.9 light years), Wolf 359 (7.8 light years) and Lalande 21185 (8.3 light years). The largest star within ten light years is Sirius, a bright main sequence star roughly twice the Sun's mass and orbited by a white dwarf called Sirius B. It lies 8.6 light years away. The remaining systems within ten light years are the binary red dwarf system Luyten 726-8 (8.7 light years) and the solitary red dwarf Ross 154 (9.7 light years). Our closest solitary sun-like star is Tau Ceti, which lies 11.9 light years away. It has roughly 80 percent the Sun's mass, but only 60 percent its luminosity. The closest known extrasolar planet to the Sun lies around the star Epsilon Eridani, a star slightly dimmer and redder than the Sun, which lies 10.5 light years away. Its one confirmed planet, Epsilon Eridani b, is roughly 1.5 times Jupiter's mass and orbits its star every 6.9 years.

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Summery

The Sun is classified as a type G2 yellow dwarf; it lies right in the middle of the main sequence in the Hertzsprung-Russell diagram - a graph which plots the brightness of stars against their surface temperatures.

The high metallicity is thought to have been crucial to the Sun's developing a planetary system, because planets are formed from accretion of "metals".

The main components of interplanetary medium namely interplanetary dust and interplanetary gas.

The outer boundary of the heliosphere, the heliopause, it is the point at which the solar wind finally terminates and is the beginning of interstellar space.

Much of our Solar System is still unknown. The Sun's gravitational field is estimated to dominate the gravitational forces of surrounding stars out to about two light years (125,000 AU).

The masses of the planets in terms of earths mass varies in the range from 0.055 (Mercury) to 318 (Jupiter). The mass of the Jupiter is greater than that of all other planets combined together.

As of September 2008, 335 bodies are formally classified as moons. They include 167 orbiting six of the eight planets, 6 orbiting three of the five dwarf planets.

Every body with an identified orbit, some as small as a kilometer across, has been identified as a moon.

The Sun's gravitational field is estimated to dominate the gravitational forces of surrounding stars out to about two light years (125,000 AU).

Our Sun resides in one of the Milky Way's outer spiral arms, known as the Orion Arm 

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There are relatively few stars within ten light years (95 trillion km) of the Sun. The closest is the triple star system Alpha Centauri, which is about 4.4 light years away.

Our closest solitary sun-like star is Tau Ceti, which lies 11.9 light years away.

The closest known extrasolar planet to the Sun lies around the star Epsilon Eridani, a star.

Exercises Fill in the blanks

1. The oldest stars contain few_______, while stars born later have more.

2. The visible part of the sun is ___________ Km across.3. The interplanetary dust can be considered as sparse

distribution of ___________ throughout the solar system.4. Earth's _____________ stops its atmosphere from being

stripped away by the solar wind.5. The heliosphere partially shields the _____________, and

planetary magnetic fields.6. Most of the material of the solar system that is not a part of the

sun itself is concentrated in the __________.7. The inner Solar System is the traditional name for the region

comprising the _____________ and asteroids.8. _________ are mostly small Solar System bodies composed

mainly of refractory rocky and metallic minerals.9. Ceres (2.77 AU) is the largest body in the asteroid belt and is

classified as a ______________ planet.

10. The Solar System is located in the ___________ Galaxy.

11. Epsilon Eridani b is one confirmed ___________ planet.

Short questions with answer

Q1. Describe the main characteristics of population I and II stars?Ans. The population stars are born in the later stages of

the evolution of universe thus; they contain more elements heavier than hydrogen and helium ("metals" in astronomical parlance) than older population II stars. 

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Q2. When and where elements heavier than hydrogen and helium are formed?

Ans. Elements heavier than hydrogen and helium were formed in the cores of ancient and exploding stars, so the first generation of stars had to die before the universe could be enriched with these atoms. The oldest stars contain few metals, while stars born later have more. 

Q3. What keep the entire sun gaseous?Ans. The high temperature of its interior and consequent

thermonuclear reactions keeps the entire sun gaseous. The tremendous pressure is produced by the great weight of the sun’s layers.

Q4. If the sun’s interior is gaseous. Why we cannot see through it?Ans. There is no distinct surface we observe optically only the level

in the sun at which the gases become opaque and prevent us from seeing deep into its interior. The temperature of that region is about 6000˚ K. Relatively, sparse outer gases extends for millions of kilometers into space in all directions. The visible part of the sun is 1,390.000 Km across. This is 109 times the diameter of the earth.

Q5. Which is the largest structure in the heliosphere?Ans. The largest structure within the heliosphere is the heliospheric

current sheet, a spiral form created by the actions of the Sun's rotating magnetic field on the interplanetary medium.

Q6. Name the disk like regions of the interplanetary medium?Ans. The interplanetary medium is home to at least two disc-like

regions of cosmic dust. The first, the zodiacal dust cloud, lies in the inner Solar System and causes zodiacal light. It was likely formed by collisions within the asteroid belt brought on by interactions with the planets. The second extends from about 10 AU to about 40 AU, and was probably created by similar collisions within the Kuiper belt.

Q7. What is the composition of the four inner or terrestrial planets?Ans. The four inner or terrestrial planets have dense, rocky

compositions, few or no moons, and no ring systems. They are composed largely of refractory minerals, such as the silicates which form their crusts and mantles, and metals such as iron and nickel, which form their cores.

Q8. Where is the main asteroid belt situated?

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Ans. The main asteroid belt occupies the orbit between Mars and Jupiter, between 2.3 and 3.3 AU from the Sun. It is thought to be remnants from the Solar System's formation that failed to coalesce because of the gravitational interference of Jupiter.

Q9. What is the structure of the Kuiper belt?Ans. The Kuiper belt, the region's first formation, is a great ring of

debris similar to the asteroid belt, but composed mainly of ice. It extends between 30 and 50 AU from the Sun. It is composed mainly of small Solar System bodies, but many of the largest Kuiper belt objects, such as Quaoar, Varuna, and Orcus, may be reclassified as dwarf planets.

Q10. What is the number of moons in the solar system?Ans. As of September 2008, 335 bodies are formally classified as

moons. They include 167 orbiting six of the eight planets, 6 orbiting three of the five dwarf planets, 104 asteroid moons, and 58 satellites of Trans-Neptunian objects, some of which will likely turn out to be dwarf planets. Some 150 additional small bodies were observed within Saturn's ring system, but they were not tracked long enough to establish orbits. Planets around other stars are likely to have natural satellites as well, although none have been observed.

Q11. What do you understand by tidal locking?Ans. The regular natural satellites in the solar system are tidally

locked to their primaries, meaning that the same side of the moon always faces the planet. The only known exception is Saturn's moon Hyperion, which rotates chaotically because of the gravitational influence of Titan.

Q12. What is the location of the solar system in the Galaxy?what is solar system's cosmic year?

Ans. The Solar System is located in the Milky Way Galaxy, a barred spiral galaxy with a diameter of about 100,000 light-years containing about 200 billion stars. Our Sun resides in one of the Milky Way's outer spiral arms, known as the Orion Arm or Local Spur. The Sun lies between 25,000 and 28,000 light years from the Galactic Centre, and its speed within the galaxy is about 220 kilometers per second, so that it completes one revolution every 225–250 million years. This revolution is known as the Solar System's cosmic year.

Q13. How the location of solar system in the galaxy does is helpful in the development of life on earth?

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Ans. The Solar System's location in the galaxy is very likely a factor in the evolution of life on Earth. Its orbit is close to being circular and is at roughly the same speed as that of the spiral arms, which means it passes through them only rarely. Since spiral arms are home to a far larger concentration of potentially dangerous supernovae, this has given Earth long periods of interstellar stability for life to evolve. The Solar System also lies well outside the star-crowded environs of the galactic centre. Near the centre, gravitational tugs from nearby stars could perturb bodies in the Oort cloud and send many comets into the inner Solar System, producing collisions with potentially catastrophic implications for life on Earth. The intense radiation of the galactic centre could also interfere with the development of complex life. Even at the Solar System's current location, some scientists have hypothesized that recent supernovae may have adversely affected life in the last 35,000 years by flinging pieces of expelled stellar core towards the Sun in the form of radioactive dust grains and larger, comet-like bodies.

Q14. Which is the closest extra solar planet?Ans. The closest known extra solar planet to the Sun lies around the

star Epsilon Eridani, a star slightly dimmer and redder than the Sun, which lies 10.5 light years away. Its one confirmed planet, Epsilon Eridani b, is roughly 1.5 times Jupiter's mass and orbits its star every 6.9 years.

Study QuestionsQ1. How we can classify the sun?Q3. Why we do not observe distinct surface on the sun?Q4. Give main characteristics of the planets.Q5. What is inner solar system?Q6. What do you understand with outer solar system?Q7. What are dwarf planets? Name and give their characteristics?Q8. What is the extent of the solar system?Q9. What are natural satellites? How they are different from the

artificial satellites?Q10. How we define moons? Write a note on the geological activities

in them?Q11. What is the immediate galactic neighborhood of solar system?Q12. Write note on:

Asteroid Belt Asteroid group

Haumea and Makemake Oorts cloud

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Asteroid Moon Centaurs Ceres Comets Eris

Pluto and Charon Scattered Disk Sedna Trans Neptunian region Trojan satellites

Chapter 4

Johannes Kepler (December 27, 1571 – November 15, 1630) was German mathematician, astronomer and astrologer, and key figure in the 17th

century scientific revolution. He is best known for his eponymous laws of planetary motion

Sir Isaac Newton FRS (4 January 1643 – 31 March 1727 [OS: 25 December 1642 – 20 March 1726]) was an  English  physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people in human history.

His 1687 publication of the Philosophiæ Naturalis Principia Mathematica (usually called the Principia) is considered to be among the most influential books in the history of science, laying the groundwork for most of classical mechanics.

Celestial Mechanics4.1 Bode’s Law:

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The discovery of Uranus brought Herschel great fame. It also brought delight to the German astronomer Johann Bode, because it fitted beautifully into the sequence of numbers announced in 1772 by David Titius, which described the approximate distance of the planets from the sun. Bode has been so impressed with Titius progression that he published it in his own introductory astronomy text and the sequence became known as “Bode’s law”. The sequence is obtained by writing down the numbers 0, 3, 6, 12, -------, each succeeding number in the sequence (after the first) being double the preceding one. If 4 is now added to each number and the sum is divided by 10, the resulting numbers are the approximate radii of the orbits of the planets in the Astronomical units, as it can be seen in Table 4.1.

Titius’ Progression Planet Actual Mean Distance (AU)

(0 + 4)/10 = 0.4 Mercury 0.387

(3 + 4)/10 = 0.7 Venus 0.732

(6 + 4)/10 = 1.0 Earth 1.000

(12 + 4)/10 = 1.6 Mars 1.524

(24 + 4)/10 = 2.8

(48+ 4)/10 = 5.2 Jupiter 5.203

(96 + 4)/10 = 10.0 Saturn 9.539

(192+ 4)/10 = 19.6 Uranus 19.190

(384 + 4)/10 = 38.8 Neptune 30.100

(768 + 4)/10 = 77.2 Pluto 39.500

Table 4.1 Bode’s law

The rule breakdown completely for Neptune and Pluto, but these planets were not known at the time of Bode. The fact that Uranus fit so well into the scheme suggested to Bode that the progression was

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law of nature which led him to expect unknown planet in the orbit of semi major axis 2.8 Au’s. Most of the Asteroids have the orbits near 2.8 Au.

4.2 Kepler’s Laws of Planetary Motion

Kepler’s first two laws of planetary motion were his most important contribution in The New Astronomy, or Commentaries on the Motion of Mars. The laws can be summarized as:

1. First Law: Each planet moves about the sun in a orbit that is an ellipse, with the sun at one focus of the ellipse.

2. Second Law: (The Law of Areas) the straight line joining a planet and the sun sweeps out equal areas in orbit al plane in equal interval of time.

At the time of publication of New Astronomy (1609) Kepler appear to have demonstrated the validity of the two laws only for the case of Mars. However, he expressed his opinion that they held also for the other planets.

4.3 Kepler’s determination of the Orbit of Mars

Kepler determined the distance between Mars and the sun or various positions of the planet in its orbit by problem of triangulation. In Figure 4.1 S represent the sun and M represent the Mars or some point in its path around the sun. Suppose we observe Mars when the earth is at E1. The angle SE1M or the earth between Mars and the sun is observable. Since the sidereal period of Mars is 687 days, after 687 days Mars will return to the point M. the earth meanwhile will have completed nearly two full revolutions around the sun and will be at E2

the angle SE2M can now be observed in exactly two years of 730½ days the earth will have returned to E1. The earth is short by 730½ - 687 = 43½ days of completing two revolutions about the sun. Thus the angleE1SE2 is known – it is the angle through which the earth moves in 43½ days. Line SE1 and SE2 are each the earth’s distance from the sun. Thus two sides and an included angle of triangle E1SE2

are known and the triangle can be solved for the side E1E2 in terms of

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distance from the earth to the sun and for the angles SE1E2 and SE2E1.

Figure 4.1 Kepler’s Method of Triangulating the distance to Mars.

Subtraction of angles SE1E2 and SE2E1 from SE1M and SE2M respectively gives the angles E2E1M and E1E2M both in the triangle E1M E2. In that later triangle since two angles and an included side are known, sides E1M and E2M and the third angle can be found. Finally, the distance of Mars from the sun (in terms of the earths distance) can be found from either triangle SE1M or SE2M.

Kepler found the distance of Mars from the sun or five points along its orbit by choosing from Tycho’s records the elongation of Mars on each of the five pair of dates separated from each other by the interval of 687 days.

4.4 Harmony of the Nature

Kepler believed in underlying the harmony in the nature, and he constantly searched for numerological relations in the celestial realm. It was a great personal triumph, therefore, that he found a simple algebraic relation between the lengths of the semi major axes of the planets’ orbits and their sidereal periods. Because the planetary axes are elliptical, the distance between a given planet and the sun varies. Now, major axis of the planet’s orbit is the sum of its maximum and minimum distances from the sun. Therefore, half of this sum, the semi major axis, can be thought of as the average distance of a

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planet from the sun. In a circular orbit, the semi major axis is simply the radius of the circle.

Kepler published his discovery in 1619 in the Harmony of the Worlds where he said.

“We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.”

The relation is known as his third or harmonic law.

4.5 Kepler’s Third Law the Square of the sidereal periods of the planets is in direct proportion to the cubes of the semi major axes of their orbits.

The Kepler’s third law can be expressed by the simple algebraic equation

P2 = Ka3

Where P represents the sidereal period of the planet, a, is the semimajor axis of the orbit, and K is the numerical constant whose value depends upon the kinds of units chosen to measure time and distance. It is convenient to use for the unit of time the earth’s period- the year-and for unit of distance the semimajor axis of the earth’s orbit, the astronomical unit (AU). With this choice of the units, K=1, and the Kepler’s third lay can be written as

P2 = a3

We see to arrive at his third law it was not necessary for Kepler to know the actual distances of the planets from the sun (say in Kilometers), only the distance in units of earth’s distance, the astronomical unit is required.

To demonstrate the Kepler’s third law considers Mars. The semimajor axis, a, of Mars orbit is 1.542 AU. The cube of 1.524 is 3.54. According to the above formula, the period of Mars in years should be the square root of 3.54or 1.88 years, a result which is in agreement with the observations. The modern values of a, P, a3 and P2for each

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six planets known at the time of Kepler is given in Table 4.2 . To limit

the accuracy of the data given , we see that Kepler’s law holds exactly , except for Jupiter

and Saturn, for which there are very slight discrepancy. Decades later, Newton gave an

explanation for discrepancies, but within the limit of accuracy of the observational data

available in 1619, Kepler was justified in considering his formula to be exact. The

Harmony of the world deals with Kepler’s attempts to associate numerical relations in the

solar system with music; indeed, he tried to derive the notes of the music played by the

planets as they move harmoniously in their orbits. The earth for example play the notes

mi, fa, mi, which he took to symbolize the ‘miseria’ (misery), fames(famine), ‘miseria’

of our planet.

Planets Semi Major Axis of the

Orbit, a (AU)

Sidereal Period, P (years)

a3 P2

Mercury 0.387 0.241 0.058 0.058

Venus 0.723 0.615 0.378 0.378

Earth 1.000 1.000 1.000 1.000

Mars 1.524 1.881 3.537 3.537

Jupiter 5.203 11.862 140.8 140.7

Saturn 9.534 29.456 867.9 867.7

Table 4.2 Observational tests for Kepler’s third Law.

4.6 Newton’s Derivations of Kepler’s Laws.

Kepler’s laws of motion are empirical laws that describe the way planets are observed to behave during their motion. On the other hand the Newton’s Laws of Motion and gravitation were proposed by him as the basis of all mechanics. Thus it should be possible to derive Kepler’s law from them. Newton did so. In fact, it was Newton derivations of the shape of the orbit of an object moving under the influence of an inverse square force that has astonished Halley.

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1. Kepler’s First Law

Consider the planer of mass mp at a distance r from the sun moving with the speed of v in a direction at right angles to the line from the planet to the sun. The centripetal force needed to keep the planet in the circular orbit, that is, at constant distance from the sun is given as

Force = mpv2/r

Now if the gravitational force between the planets and the sun happens to be greater than the force given by the above equation. Then the planet will receive more acceleration than is necessary to keep it ion the circular orbit and it will move in somewhat closer to the sun. As it does so, its speed will increase just as the speed of falling stone increases as it approaches the ground. Due to planet’s increased speed and the decreased distance from the sun. A greater centripetal force is required to keep it at constant distance from the sun. Eventually, as the planet continues to sweep in closer to the sun at higher and higher speed. A point will be reached at which the gravitational force between the two is no longer sufficient to produce sufficient centripetal acceleration to keep the Planet from moving out away from the sun. Thus the planet will move outwards it rounds the sun until it has reached the position where the gravitational acceleration is again greater than the circular centripetal acceleration and this process is repeated. If the situation were reversed, and planet were moving fast enough for the centripetal force required for the circular motion to be greater than the gravitational attraction, the planet will move outward and consequently slow down until the gravitational force could pull it back again.Thus we see qualitatively, how the planet may follow an elliptical orbit, if however, a planet had a high enough speed the gravitational force between it and the sun might never be enough to provide sufficient centripetal force to hold the planet in the solar system, and the planet will move off into the space. Its orbit would then be a hyperbola rather than a closed, elliptical path as shown in Figure 4.2. There is a certain critical speed, which depends on planets distance

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from the sun or which the planet can just barely escape the solar system along a parabolic orbit. This critical speed is called parabolic velocity or velocity of escape. In order to prove that the gravitational force between the sun and a planet must result in an orbit for the planet that is a circle, an ellipse, parabola or hyperbola. To solve this problem Newton used his fluxions, which we now call differential calculus. He showed in fact, that the gravitational interaction between any two bodies would result in an orbital motion of each body about the other that is some form of conic section. Circular and the parabolic orbits require theoretically precise speed that would not be expected to occur in nature, thus we would not expect to find a planet (or other object) with exactly a circular or parabolic orbit. The later divides the family of elliptical (closed) from the family of hyperbolic (open) orbits that actually occur in nature The planets, of course, do not have hyperbolic orbits or they would long since have receded into interstellar space; their orbits then must be elliptical, as found by Kepler.

Figure 4.2 Relative hyperbolic Orbits.

2. Kepler’s Second Law Consider a planet at A revolving about the sun at S as indicated in Figure 4.3. In short interval of time the planet’s forward velocity would ordinarily carry it to B. However, the gravitational pull between it and the sun accelerates it to C, since we are considering a very brief interval of time. We can regard the acceleration of the planet as being along the direction BC parallel to AS, the direction of from the planet to the sun at the beginning of the instant. The planet now has the velocity along the direction of AC. In the next brief interval of time,

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equal in length to the first interval, the planet would ordinarily continue moving in a straight line or a constant speed and would end up at D, along the extension of AC so that the distance CD was equal to the distance AC. However, again the sun accelerates the planet towards it (now in the direction Cs) so the planet actually moves along CE.Consider AC and CD to be basis of the triangles ASC and CSD, respectively. Since AC = CD, the two triangles have equal bases. They also have same altitudes. - The perpendicular distance of S from AD or its extension. Thus triangles ASC and CSD having equal bases and altitudes have equal areas.

Figure 4.3 Geometrical Proof of the law of areas.

Since triangles ASC and CSE are both equal in area to the triangle SCD, they are equal in area to each other. These are the area swept out by a line from the planet to the sun in two successive intervals of time. Many such brief intervals of time can be combined too show that the areas swept out any two equal intervals of time are equal, thus Kepler’s second law is verified.

3. Kepler’s Third LawFor each of two mutually revolving bodies the gravitational attraction between the two provides the centripetal acceleration to keep them in circular orbits. If m1 and m2 be the masses of the bodies having distances r1 and r2 from the common center of mass, they are separated by the distance r1 + r2 and we can equate the gravitational force to centripetal force for each body. We have

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For body 1 G m1m2 = m14π2 r1

(r1 + r2)2 P2

For body 2 G m1m2 = m24π2 r2

(r1 + r2)2 P2

If we cancel out the masses common to each side of each equation and add the two equations we obtain

G m1+ m2 = 4π2 (r1 + r2) (r1 + r2)2 P2

Or (m1+ m2) P2 = 4π2 (r1 + r2)3

G

Since (r1 + r2) is the distance between the two bodies we recognize it, in case of a planet going around the sun in a circular orbit as a semimajor axis a of the relative orbit . Then the above equation looks the same as the formula for Kepler’s third law (P2 = a3) except for the factor (m1+ m2) and 4π2/G. The later is simply a constant of proportionality. If the proper units are chosen for the distance and time, G will take such a value that 4π2/G.will equal unity. We discuss below why Kepler was not aware of the factor (m1+ m2).

Newton derived his equations not only for the planets moving about the sun but also for any pair of mutually revolving bodies- two stars, a planet and a satellite, or even a plate and a spoon revolving about each other in the space.

Newton’s version of Kepler’s third law differ from the original in that it contains a factor the sum of the masses of two bodies. It becomes clear why Kepler was not aware of that term if we note that we can consider the sun and the earth to be the pair of mutually revolving bodies. We know that the mass of the sun is about 300,000 times that

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of the earth. Thus the combined mass of the sun and the earth is, to all intend and purposes the mass of the sun itself, the earths mass being negligible in comparison. Suppose we chose the mass of the sun to our unit of mass. Then, in the earth - sun system (m1+ m2) = 1. Furthermore, the sum of masses of the sun and any other planet is also very nearly unity. Even Jupiter the most massive planet, has only 1/1000 of the mass of the sun, for the sun and Jupiter (m1+ m2) = 1.001, a number so nearly equal to 1.000 that Kepler was unable to detect the difference from Tycho’s observations. The fact that the masses of Jupiter and Saturn are not completely negligible compared to the sun accounts, in part, for the slight discrepancies in the Kepler’s versions of Third law as applied to Jupiter and Saturn (See Table 4.2) thus if we apply the equation Newton derived to the mutual revolution of the sun an a planet, and chose years and astronomical units as units of time and distance. And the solar mass as the unit of mass. Newton’s equation reduces to

(m1+ m2) P2 = (1) P2 = a3

.

4.7 Restatement of the Kepler’s law

The three laws of planetary motion of Kepler can be restated in their more general form as derived by Newton.

Kepler’s First Law

If two bodies interact gravitationally, each will describe an orbit that is a conic section about the common center of mass of the pair. In particular, if the bodies are permanently associated, their orbit will be ellipse. If they are not permanently associated, their orbits will be hyperbola.

Kepler’s Second Law

If two bodies revolve about each other under the influence of a central force (whether or not in a closed elliptical orbit), a line joining them sweeps out equal areas in the orbital plane in equal interval of time.

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Kepler’s Third LawIf the bodies revolve mutually about each other, the sum of their masses times the square of their period of mutual revolution is in proportion to the cube of the semimajor axis of the relative orbit of one about the other.

In metric units the algebraic formulation of Newton’s version of Kepler’s third law is

(m1+ m2) P2 = 4π2 (r1 + r2)3

GWhere, G is the constant of gravitation. If the units of length, mass and time are centimeters, grams, and seconds, respectively G has the value 6.67 x 10-8.If either of the sets of units shown in Table 4.3 is used the law becomes

(m1+ m2) P2 = a3

I II

Unit of (m1+ m2) Sun’s mass + earth’s mass earth’s mass + Moon’s mass

Units of P Sidereal Year Sidereal month

Units of a Astronomical unit Mean distance of moon from

earth

Table 4.3 Examples of system of units for which 4π2 = 1 G4.8 Masses of the planets

The only means of measuring the masses of the astronomical bodies is to study the way in which they react gravitationally with other bodies. Newton’s derivation of Kepler’s third law, which involves the term involving the sum of masses of the revolving bodies, is most useful for the purpose.

Consider a planet like Jupiter that has one or more satellites revolving about it. We can select on of these satellites and regard that satellite

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and its parent planet as a pair of mutually revolving bodies. We measure the period of revolution of the satellite (say sidereal months) and the distance of the satellite from the planet (in terms of distance of the moon from the earth) and insert these values in the equation

(m1+ m2) = a3

P2

Since both a and p are observed, we can immediately calculate the combined mass of the planet and its satellite. Obviously most of the mass belong to the planet; its satellite will be very small compared to it. Thus, m1+ m2 is, essentially the mass of the planet in terms of mass of the earth.To demonstrate it numerically, let us consider, Deimos the outermost satellite of Mars, has the sidereal period of 1.262 days and the mean distance from the center of mass of 23,500 kilometers. In sidereal months the period of satellite is 1.262/27.3 = 0.0462 in terms of distance of the moon from the earth. Deimos has the distance from the center of mass

23500 = 0.0611384,404

Thus the mass of the Mars plus the mass of the Deimos

mMars + mDeimos = (0.0611)3

(0.0462)2

= 2.8 x 10-4 = 0.11 x earths Mass 2.13 x 10-3

Since the Deimos is very small satellite (only about 13 Km across) its mass can be neglected compared to that of the Mars, and we find that the Mars has the mass just over one tenth of the earth.

4.9 Newton’s law of Universal Gravitation For Newton’s hypothesis of universal attraction to be correct, it must be an attractive force between all pairs of objects everywhere where the value is given by the same mathematical formula as that for the

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force between the planet and the sun. Thus the force on two bodies with masses m1 and m2 separated by a distance d is given by

F = G m1m2/d2

Here G is constant of proportionality in the equation, is a number called the constant of gravitation whose value depends on units of mass, distance and force used. The actual value of G has been determined by laboratory measurements of the attractive force between two material bodies. If metric units are used G has numerical value of 6.67 x 10-8.The above equation expresses Newton’s law of universal gravitation which is stated as “Between any two objects anywhere in the space their exists a force of attraction that is in proportion to the product of the masses of the objects and inverse proportion to the square of the distance between them”.4.10 Mass of the EarthThe gravitational force, between a object of mass m on the earth and the earth itself of mass M is equal to the constant of gravitation times the product of the masses m and M divided by the square of the distance from the object to the center of the earth. The later distance is just the radius of the earth, R. this force is attraction between the earth and the body on its surface is the bodies weight that is,

W = GmM/R2

However, in the vicinity of another gravitating body, his weight is determined the attraction between the bodies. If the object is dropped from the height, the downward acceleration is equivalent to force acting on it, that is, weight is divided by its mass

(g) acceleration = W/m = GM/R2

Or M = g R2/G

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Thus the mass of the earth can be calculated. As the values of g, and R are known.

Summery

1. Kepler’s first two laws of planetary motion were his most important contribution in The New Astronomy

2. First Law: Each planet moves about the sun in a orbit that is an ellipse, with the sun at one focus of the ellipse.

3. Second Law: (The Law of Areas) the straight line joining a planet and the sun sweeps out equal areas in orbit al plane in equal interval of time.

4. Kepler determined the distance between Mars and the sun or various positions of the planet in its orbit by problem of triangulation.

5. Kepler believed in underlying the harmony in the nature, and he constantly searched for numerological relations in the celestial realm.

6. Kepler’s third Law states that the square of the sidereal periods of the planets is in direct proportion to the cubes of the semi major axes of their orbits.

7. The Harmony of the world deals with Kepler’s attempts to associate numerical relations in the solar system with music

8. Newton’s law of universal gravitation which is stated as “Between any two objects anywhere in the space their exists a force of attraction that is in proportion to the product of the masses of the objects and inverse proportion to the square of the distance between them”.

Exercises Fill in the blanks

1. The sequence of numbers announced in 1772 by David Titius, which described the approximate distance of the planets from the _________.

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2. Titius progression that he published it in his own introductory astronomy text and __________ became known as “Bode’s law”.

3. Each planet moves about the sun in a orbit that is an ellipse, with the sun at one focus of the __________.

4. The straight line joining a __________ and the sun sweeps out equal areas in orbit al plane in equal interval of time.

5. Kepler believed in underlying the harmony in the nature, and he constantly searched for ___________ relations in the celestial realm.

6. Because the planetary axes are __________, the distance between a given planet and the sun varies.

7. The Square of the ___________ of the planets is in direct proportion to the _________ of the semi major axes of their orbits.

8. If the bodies are permanently associated, their orbit will be _________. If they are not permanently associated, their orbits will be ____________.

9. (m1+ m2) P2 = __________.

10. If metric units are used Universal Gravitation (G) has numerical value of ___________.

Short questions with answer

Q1. How Titus sequence can be obtained?Ans. David Titius, sequence which described the approximate

distance of the planets from the sun also known as “Bode’s law” is obtained by writing down the numbers 0, 3, 6, 12, -------, each succeeding number in the sequence (after the first) being double the preceding one. If 4 is now added to each number and the sum is divided by 10, the resulting numbers are the approximate radii of the orbits of the planets in the Astronomical units,

Q2. What is Kepler’s first law? What correction did the Newton introduced?

Ans. According to Kepler’s first law each planet moves about the sun in an orbit that is an ellipse, with the sun at one focus of the ellipse. On the other hand the Newton applied Laws of Motion

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and gravitation as proposed by him and modified the Kepler’s laws according to the modification the law states that “If two bodies interact gravitationally, each will describe an orbit that is a conic section about the common center of mass of the pair. In particular, if the bodies are permanently associated, their orbit will be ellipse. If they are not permanently associated, their orbits will be hyperbola”.

Q3. What is Kepler’s law of areas?Ans. The Kepler’s second also known as Law of areas states that the

straight line joining a planet and the sun sweeps out equal areas in orbit al plane in equal interval of time.

Q3. What is Kepler’s Third law?Ans. If the bodies revolve mutually about each other, the sum of their

masses times the square of their period of mutual revolution is in proportion to the cube of the semimajor axis of the relative orbit of one about the other.

Q4. How we can measure the masses of the astronomical bodies?Ans. The only means of measuring the masses of the astronomical

bodies is to study the way in which they react gravitationally with other bodies.

Study QuestionsQ1. What is the eccentricity of the orbit of the planet whose distance

from the sun varies from 180 million to 220 million kilometers?Q3. The earth’s distance from the sun varies from 147.2 million to

152.1 million kilometers. What is the eccentricity of the object?Q4. Consider Kepler’s third law as given in section 4.5, carefully

explain why K= 1 when a is measured in astronomical units and p2 in years?

Q5. What is the period of the planet whose orbit has semi major axis of 4.0 AU?

Q6. What would be the distance from the sun of a planet whose period is 45.66 days?

Q7. Suppose Kepler’ law applies to the motion of Jupiter’s satellite Io round that planet, and that one of the satellite has period of 5.196 times as long as another one. What will be the ratio of semimajor axes of their orbits?

Q8. Why does the Newton’s version of Kepler’s third law has the form (m1+ m2) P2 = a3 ?

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Q9. A cow attempted to jump over the moon but landed into the orbit around the moon. Describe how the cow could be used to determine the mass of the moon?

Stars

Unit III

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Chapter 5Sir Frederick William Herschel, (15 November 1738 – 25 August 1822) was a British astronomer, technical expert, and a composer.. Herschel became most famous for the discovery of the planet Uranus in addition to several of its major moons such as Titania and Oberon. He also discovered infrared radiation.

StarsHistorically, stars have been important to civilizations throughout the world. They have been part of religious practices and for celestial navigation and orientation. As has been said by the poet Ralph Waldo Emerson

“Teach me your mood, O patient stars.

Who climb each night, the ancient sky.

leaving on space no shade, no scars, no trace of age, no fear to die.”

Many ancient astronomers believed that stars were permanently affixed to a heavenly sphere, and that they were immutable. By convention, astronomers grouped stars into constellations and used them to track the motions of the planets and the inferred position of the Sun. The motion of the Sun against the background stars (and the horizon) was used to create calendars, which could be used to regulate agricultural practices.

The Gregorian calendar, currently used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to the nearest star, the Sun. The oldest accurately dated

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star chart appeared in Ancient Egypt in 1,534 BC. The Greek astronomer Aristillus created the first star catalogue in approximately 300 BC, with the help of Timocharis. Ptolemy's star catalogue was based on an earlier record by Hipparchus from the 2nd century BC.

Figure 5.1: People have seen patterns in the stars since ancient times. This 1690 depiction of the constellation of Leo, the lion, is by Johannes Hevelius.

Hipparchus is known for the discovery of the first nova (new star). Islamic astronomers gave to many stars Arabic names which are still used today, and they invented numerous astronomical instruments which could compute the positions of the stars. In the 11th century, Abū Rayhān al-Bīrūnī described the Milky Way galaxy as multitude of fragments having the properties of nebulous stars, and also gave the latitudes of various stars during a lunar eclipse in 1019.

In spite of the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. Early European astronomers such as Tycho Brahe identified new stars in the night sky (later termed novae), suggesting that the heavens were not immutable. In 1584 Giordano Bruno suggested that the stars were actually other suns, and may have other planets, possibly even Earth-like, in orbit around them, an idea that had been suggested earlier by such ancient Greek philosophers as Democritus and

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Epicurus. By the following century the idea of the stars as distant suns was reaching a consensus among astronomers.To explain why these stars exerted no net gravitational pull on the solar system, Isaac Newton suggested that the stars were equally distributed in every direction, an idea prompted by the theologian Richard Bentley. The Italian astronomer Geminiano Montanari recorded observing variations in luminosity of the star Algol in 1667. Edmond Halley published the first measurements of the proper motion of a pair of nearby "fixed" stars, demonstrating that they had changed positions from the time of the ancient Greek astronomers Ptolemy and Hipparchus. The first direct measurement of the distance to a star (61 Cygni at 11.4 light-years) was made in 1838 by Friedrich Bessel using the parallax technique. Parallax measurements demonstrated the vast separation of the stars in the heavens.

William Herschel was the first astronomer to attempt to determine the distribution of stars in the sky. During the 1780s, he performed a series of gauges in 600 directions, and counted the stars observed along each line of sight. From this he deduced that the number of stars steadily increased toward one side of the sky, in the direction of the Milky Way core. His son John Herschel repeated this study in the southern hemisphere and found a corresponding increase in the same direction. In addition to his other accomplishments, William Herschel is also noted for his discovery that some stars do not merely lie along the same line of sight, but are also physical companions that form binary star systems.

The science of stellar spectroscopy was pioneered by Joseph von Fraunhofer and Angelo Secchi. By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines—the dark lines in a stellar spectra due to the absorption of specific frequencies by the atmosphere. In 1865 Secchi began classifying stars into spectral types. However, the modern version of the stellar classification scheme was developed by Annie J. Cannon during the 1900s.

Observation of double stars gained increasing importance during the 19th century. In 1834, Friedrich Bessel observed changes in the proper motion of the star Sirius, and inferred a hidden companion.

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Edward Pickering discovered the first spectroscopic binary in 1899 when he observed the periodic splitting of the spectral lines of the star Mizar in a 104 day period. Detailed observations of many binary star systems were collected by astronomers such as William Struve and S. W. Burnham, allowing the masses of stars to be determined from computation of the orbital elements. The first solution to the problem of deriving an orbit of binary stars from telescope observations was made by Felix Savary in 1827. The twentieth century saw increasingly rapid advances in the scientific study of stars. The photograph became a valuable astronomical tool. Karl Schwarzschild discovered that the color of a star, and hence its temperature, could be determined by comparing the visual magnitude against the photographic magnitude. The development of the photoelectric photometer allowed very precise measurements of magnitude at multiple wavelength intervals.

In 1921 Albert A. Michelson made the first measurements of a stellar diameter using an interferometer on the Hooker telescope. Important conceptual work on the physical basis of stars occurred during the first decades of the twentieth century.

In 1913, the Herhzsprung-Russell diagram was developed, propelling the astrophysical study of stars. Successful models were developed to explain the interiors of stars and stellar evolution. The spectra of stars were also successfully explained through advances in quantum physics. This allowed the chemical composition of the stellar atmosphere to be determined. With the exception of supernovae, individual stars have primarily been observed in our Local Group of galaxies, and especially in the visible part of the Milky Way (as demonstrated by the detailed star catalogues available for our galaxy). But some stars have been observed in the M100 galaxy of the Virgo Cluster, about 100 million light years from the Earth. In the Local Supercluster it is possible to see star clusters, and current telescopes could in principle observe faint individual stars in the Local Cluster—the most distant stars resolved have up to hundred million light years away (see Cepheids). However, outside the Local Supercluster of galaxies, neither individual stars nor clusters of stars have been observed. The only exception is a faint image of a large star cluster containing hundreds of thousands of stars located one

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billion light years away—ten times the distance of the most distant star cluster previously observed.

5.1 Characteristics

Almost everything about a star is determined by its initial mass, including essential characteristics such as luminosity and size, as well as the star's evolution, lifespan, and eventual fate. Age of most stars is between 1 billion and 10 billion years old. Some stars may even be close to 13.7 billion years old—the observed age of the universe. The oldest star yet discovered, HE 1523-0901, is an estimated 13.2 billion years old. The more massive the star, the shorter its lifespan, primarily because massive stars have greater pressure on their cores, causing them to burn hydrogen more rapidly. The most massive stars last an average of about one million years, while stars of minimum mass (red dwarfs) burn their fuel very slowly and last tens to hundreds of billions of years.

Figure 5.2 The Sun is the nearest star to Earth

Thus we can say that a star is a massive, luminous ball of plasma that is held together by gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth. Other stars are visible in the night sky, when they are not outshone by the Sun. Historically, the most prominent stars on the celestial sphere were grouped together into constellations, and the brightest stars gained proper names. Extensive catalogues of stars have been assembled by astronomers, which provide standardized designations. For most of its life, a star shines due to thermonuclear fusion in its core releasing energy that traverses the star's interior and then radiates

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into outer space. Almost all elements heavier than hydrogen and helium were created by fusion processes in stars. Astronomers can determine the mass, age, chemical composition and many other properties of a star by observing its spectrum, luminosity and motion through space. The total mass of a star is the principal determinant in its evolution and eventual fate. Other characteristics of a star are determined by its evolutionary history, including the diameter, rotation, movement and temperature. A plot of the temperature of many stars against their luminosities, known as a Hertzsprung-Russell diagram (H–R diagram), allows the age and evolutionary state of a star to be determined. A star begins as a collapsing cloud of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. Once the stellar core is sufficiently dense, some of the hydrogen is steadily converted into helium through the process of nuclear fusion. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective processes. The star's internal pressure prevents it from collapsing further under its own gravity. Once the hydrogen fuel at the core is exhausted, those stars having at least 0.4 times the mass of the Sun expand to become a red giant, in some cases fusing heavier elements at the core or in shells around the core. The star then evolves into a degenerate form, recycling a portion of the matter into the interstellar environment, where it will form a new generation of stars with a higher proportion of heavy elements’ Binary and multi-star systems consist of two or more stars that are gravitationally bound, and generally move around each other in stable orbits. When two such stars have a relatively close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, such as a cluster or a galaxy.

5.2 Star designations Astronomical naming conventions, and Star catalogue

The concept of the constellation was known to exist during the Babylonian period. Ancient sky watchers imagined that prominent arrangements of stars formed patterns, and they associated these with particular aspects of nature or their myths. Twelve of these formations lay along the band of the ecliptic and these became the basis of astrology. Many of the more prominent individual stars were

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also given names, particularly with Arabic or Latin designations. As well as certain constellations and the Sun itself, stars as a whole have their own myths. To the Ancient Greeks, some "stars," known as planets (Greek πλανήτης (planētēs), meaning "wanderer"), represented various important deities, from which the names of the planets Mercury, Venus, Mars, Jupiter and Saturn were taken. (Uranus and Neptune were also Greek and Roman gods, but neither planet was known in Antiquity because of their low brightness. Their names were assigned by later astronomers). Circa 1600, the names of the constellations were used to name the stars in the corresponding regions of the sky. The German astronomer Johann Bayer created a series of star maps and applied Greek letters as designations to the stars in each constellation. Later a numbering system based on the star's right ascension was invented and added to John Flamsteed's star catalogue in his book "Historia coelestis Britannica" (the 1712 edition), whereby this numbering system came to be called Flamsteed designation or Flamsteed numbering.

The only body which has been recognized by the scientific community as having the authority to name stars or other celestial bodies is the International Astronomical Union (IAU). A number of private companies (for instance, the "International Star Registry") purport to sell names to stars; however, these names are neither recognized by the scientific community nor used by them, and many in the astronomy community view these organizations as frauds preying on people ignorant of star naming procedure.

5.3 Units of measurement

Most stellar parameters are expressed in SI units by convention, but CGS units are also used (e.g., expressing luminosity in ergs per second). Mass, luminosity, and radii are usually given in solar units, based on the characteristics of the Sun:

solar mass:  kgsolar luminosity:  wattssolar radius: m

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Large lengths, such as the radius of a giant star or the semi-major axis of a binary star system, are often expressed in terms of the astronomical unit (AU)—approximately the mean distance between the Earth and the Sun (150 million km or 93 million miles).

5.4 Stellar Magnetic field

The magnetic field of a star is generated within regions of the interior where convective circulation occurs. This movement of conductive plasma functions like a dynamo, generating magnetic fields that extend throughout the star. The strength of the magnetic field varies with the mass and composition of the star, and the amount of magnetic surface activity depends upon the star's rate of rotation. This surface activity produces starspots, which are regions of strong magnetic fields and lower than normal surface temperatures. Coronal loops are arching magnetic fields that reach out into the corona from active regions. Stellar flares are bursts of high-energy particles that are emitted due to the same magnetic activity. Young, rapidly rotating stars tend to have high levels of surface activity because of their magnetic field. The magnetic field can act upon a star's stellar wind;

Figure 5.3 Surface magnetic field of SU   Aur (a young star of T Tauri type), reconstructed by means of Zeeman-Doppler imaging

However, functioning as a brake to gradually slow the rate of rotation as the star grows older. Thus, older stars such as the Sun have a much slower rate of rotation and a lower level of surface activity. The activity levels of slowly rotating stars tend to vary in a cyclical manner

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and can shut down altogether for periods. During the Maunder minimum, for example, the Sun underwent a 70-year period with almost no sunspot activity.

5.5 Stellar Mass

One of the most massive stars known is Eta Carinae, with 100–150 times as much mass as the Sun; its lifespan is very short—only several million years at most. A recent study of the Arches cluster suggests that 150 solar masses is the upper limit for stars in the current era of the universe. The reason for this limit is not precisely known, but it is partially due to the Eddington luminosity which defines the maximum amount of luminosity that can pass through the atmosphere of a star without ejecting the gases into space.

Figure 5.4 The reflection nebula NGC 1999 is brilliantly illuminated by V380 Orionis (center), a variable star with about 3.5 times the mass of the Sun. NASA image

The first stars to form after the Big Bang may have been larger, up to 300 solar masses or more, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive, population III stars is long extinct, however, and currently only theoretical. With a mass only 93 times that of Jupiter, AB Doradus C, a companion to AB Doradus A, is the smallest known star undergoing nuclear fusion in its core. For stars with similar metallicity to the Sun, the theoretical minimum mass the star can have, and still undergo fusion at the core, is estimated to be about 75 times the mass of Jupiter. When the metallicity is very low, however, a recent study of the faintest stars found that the minimum star size seems to be about 8.3% of the solar mass, or about 87 times the

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mass of Jupiter. Smaller bodies are called brown dwarfs, which occupy a poorly defined grey area between stars and gas giants. The combination of the radius and the mass of a star determines the surface gravity. Giant stars have a much lower surface gravity than main sequence stars, while the opposite is the case for degenerate, compact stars such as white dwarfs. The surface gravity can influence the appearance of a star's spectrum, with higher gravity causing a broadening of the absorption lines.

5.6 Stellar rotation

The rotation rate of stars can be approximated through spectroscopic measurement, or more exactly determined by tracking the rotation rate of starspots. Young stars can have a rapid rate of rotation greater than 100 km/s at the equator. The B-class star Achernar, for example, has an equatorial rotation velocity of about 225 km/s or greater, giving it an equatorial diameter that is more than 50% larger than the distance between the poles. This rate of rotation is just below the critical velocity of 300 km/s where the star would break apart. By contrast, the Sun only rotates once every 25 – 35 days, with an equatorial velocity of 1.994 km/s. The star's magnetic field and the stellar wind serve to slow down a main sequence star's rate of rotation by a significant amount as it evolves on the main sequence. Degenerate stars have contracted into a compact mass, resulting in a rapid rate of rotation. However they have relatively low rates of rotation compared to what would be expected by conservation of angular momentum—the tendency of a rotating body to compensate for a contraction in size by increasing its rate of spin. A large portion of the star's angular momentum is dissipated as a result of mass loss through the stellar wind. In spite of this, the rate of rotation for a pulsar can be very rapid. The pulsar at the heart of the Crab nebula, for example, rotates 30 times per second. The rotation rate of the pulsar will gradually slow due to the emission of radiation.

5.7 Temperature

The surface temperature of a main sequence star is determined by the rate of energy production at the core and the radius of the star and is often estimated from the star's color index. It is normally given as the effective temperature, which is the temperature of an idealized

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black body that radiates its energy at the same luminosity per surface area as the star. Note that the effective temperature is only a representative value, however, as stars actually have a temperature gradient that decreases with increasing distance from the core. The temperature in the core region of a star is several million Kelvin. The stellar temperature will determine the rate of energization or ionization of different elements, resulting in characteristic absorption lines in the spectrum. The surface temperature of a star, along with its visual absolute magnitude and absorption features, is used to classify a star (see Table 5.1). Massive main sequence stars can have surface temperatures of 50,000 K. Smaller stars such as the Sun have surface temperatures of a few thousand K. Red giants have relatively low surface temperatures of about 3,600 K, but they also have a high luminosity due to their large exterior surface area.

5.8 Radiation

The energy produced by stars, as a by-product of nuclear fusion, radiates into space as both electromagnetic radiation and particle radiation. The particle radiation emitted by a star is manifested as the stellar wind (which exists as a steady stream of electrically charged particles, such as free protons, alpha particles, and beta particles, emanating from the star’s outer layers) and as a steady stream of neutrinos emanating from the star’s core. The production of energy at the core is the reason why stars shine so brightly: every time two or more atomic nuclei of one element fuse together to form an atomic nucleus of a new heavier element, gamma ray photons are released from the nuclear fusion reaction. This energy is converted to other forms of electromagnetic energy, including visible light, by the time it reaches the star’s outer layers. The color of a star, as determined by the peak frequency of the visible light, depends on the temperature of the star’s outer layers, including its photosphere. Besides visible light, stars also emit forms of electromagnetic radiation that are invisible to the human eye. In fact, stellar electromagnetic radiation spans the entire electromagnetic spectrum, from the longest wavelengths of radio waves and infrared to the shortest wavelengths of ultraviolet, X-rays, and gamma rays. All components of stellar electromagnetic radiation, both visible and invisible, are typically significant. Using the stellar spectrum, astronomers can also determine the surface temperature, surface gravity, metallicity and rotational velocity of a

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star. If the distance of the star is known, such as by measuring the parallax, then the luminosity of the star can be derived. The mass, radius, surface gravity, and rotation period can then be estimated based on stellar models. (Mass can be measured directly for stars in binary systems. The technique of gravitational microlensing will also yield the mass of a star. With these parameters, astronomers can also estimate the age of the star.

5.9 Luminosity

In astronomy, luminosity is the amount of light, and other forms of radiant energy, a star radiates per unit of time. The luminosity of a star is determined by the radius and the surface temperature. However, many stars do not radiate a uniform flux—the amount of energy radiated per unit area—across their entire surface. The rapidly rotating star Vega, for example, has a higher energy flux at its poles than along its equator. Surface patches with a lower temperature and luminosity than average are known as starspots. Small, dwarf stars such as the Sun generally have essentially featureless disks with only small starspots. Larger, giant stars have much bigger, much more obvious starspots, and they also exhibit strong stellar limb darkening. That is, the brightness decreases towards the edge of the stellar disk. Red dwarf flare stars such as UV Ceti may also possess prominent starspot features.

5.10 Stellar Spectra: A Classification

When the spectra of different stars were observed, it was found that they differ greatly among themselves. In 1863 the Jesuit astronomer Angelo Secchi categorized stars into four groups according to general arrangement of the dark lines in their spectra. Srcchi’s scheme was subsequently modified and augmented, till date we recognize seven such principal spectral classes.

5.11 Spectral Sequence

As we know, each dark line in a stellar spectrum is due to the presence of a particular chemical element in the atmosphere of the star observed, it might seem, therefore, that the stellar spectra differ from each other because of difference in the chemical make up of the

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star. Actually, the difference in the stellar spectra is due mostly to the widely differing temperatures in the outer layers of the various stars. Hydrogen, for example is by far most abundant element in all stars, except probably in those at the advanced stage of evolution. In the atmosphere of very hottest stars, hydrogen is completely ionized and can therefore produce no absorption lines. In the atmosphere of the coolest star hydrogen is neutral and can produce absorption lines, but in these stars practically all of the hydrogen atoms are in lowest energy state, and can absorb only those photons that can lift them from first energy level to the higher ones; the photons so absorbed produce the Layman series of absorption lines, which lies in the unobservable ultraviolet part of the spectrum. In the stellar atmosphere with a temperature of about 10,000 K, many hydrogen atoms are not ionized and appreciable number of these are excited to second energy level, from which they can absorb additional photons and rise to higher level of excitation. These photons correspond to the wavelength of Balmer series which is in the part of spectrum that is readily observable. Absorption lines due to hydrogen. Therefore are strongest in the spectra of the stars whose atmosphere have temperatures near 10,000 K and they are less conspicuous in the spectra of both hotter and cooler stars, even though the hydrogen is roughly equally abundant in all the stars. Similarly, every other chemical element in each of its possible stage of ionization has a characteristic temperature at which it is most effective in producing the absorption lines in the observable part of the spectrum. Once it is ascertained how the temperature of stars can determine the physical states of the gases in its outer layers, and thus their ability to produce absorption lines. We need only to observe what patterns of absorption lines are present in the spectrum of a star to learn its temperature. We can therefore arrange the seven classes of the stellar spectra in continuous sequence in order of decreasing temperature. In the hottest stars with the temperature over 25000 K only lines of ionized helium and highly ionized atoms of other elements are conspicuous. Hydrogen lines are shortest in stars with atmospheric temperature of about 10,000 K. Ionized metals provide the most conspicuous lines in the stars with temperatures from 6000 to 8000 K. Lines of neutral metals are strongest in somewhat cooler stars. In the coolest stars ( below 4000 K) bands of some molecules are very strong, The most important among the molecules bands are those due to titanium oxide, a tenacious chemical compound which

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can exist at a temperature of cooler stars. The sequence of spectral types is summarized in Table 5.1

Hot star types O,B,A – are sometimes referred to as having early spectral types, The spectral classes of the stars G,K,M- as late spectral types. The spectral classes of stars listed in the table can be subdivided into tenths, thus a star of spectral class A5 is midway in the range of A- type stars that is halfway between the stars of type A0 and F0. The sun is of spectral class G2- two tenth of the way from class G0 to K0. The spectral sequence ranging smoothly from O to M with decreasing temperature was established through the classification of hundreds of thousands of stellar spectra in years 1918 to 1924 by astronomers at Harvard University; pioneered by Edward Pickering and a woman astronomer with the unlikely name of Annie Cannon, among others. Famous American astronomer Henry Norris Russel proposed a scheme by which every student can remember the order of classes in the spectral sequence. The class letters are the first letters of the words “ Oh, Be A Fine Girl, Kiss Me!”

Spectral Class

Color Approximate Temperature

(K)

Principal Features Stellar Examples

O Blue › 25,000 Relatively few absorption lines in observable spectrum. Lines of ionized helium, doubly ionized nitrogen, triply ionized silicon, and other lines of highly ionized atoms. Hydrogen lines appears only weekly

10 LacertaeZeta Ophiuchi

B Blue 11,000-25,000 Lines of neutral helium, singly and doubly ionized silicon, singly ionized oxygen and magnesium. Hydrogen lines more pronounced than the O type stars

Rigel Spica

A Blue 7,500- 11,000 Strong lines of hydrogen. Also lines of singly ionized magnesium, silicon, iron, titanium, calcium and others. Lines of some neutral metals show weakly

Sirius VegaAltair

F Blue to White

6000-7500 Hydrogen lines are weaker than in A-type stars but are still conspicuous. Lines of singly ionized calcium. Iron and chromium and also lines of neutral iron and chromium are present, as are lines of other neutral metals

Canopus Procyon

G White to Yellow

5000-6000 Lines of ionized calcium are most conspicuous spectral features. Many lines of ionized and neutral metals are present. Hydrogen lines are weak even than in F-type stars. Bands of CH, the hydrocarbon radicals, are strong

Sun Capella

K Orange to Red

3500-5000 Lines of neutral metal predominate. The CH bands are still present.

Arcturus Aldebaran

M Red ‹ 3500 Strong lines of neutral metals and molecular bands of titanium oxide dominate

Betelgeuse Anteres

Table 5.1 Classification of stars according to their spectra

Originally there were a number of spectral classes from A-Q, designating stars according to the complexity of their emission lines.

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That classification was dropped in favor of the simplified version we see today, which orders stars according to their color/temperature, but maintains the letter names from the old classification. Recent decades have seen the introduction of a few new spectral classes, to cover interstellar oddballs are shown in Table 5.2

W Wolf-Rayet Stars(Blue)C Carbon stars (Red) S Brown Dwarfs

Table 5.2 The major luminosity classes

Stars in the Harvard system are further classified according to their luminosity, a measurement based on the brightness of the star, which gives us some idea of its mass. Stars may also be classified by the luminosity effects found in their spectral lines, which correspond to their spatial size and is determined by the surface gravity. As shown in Table 5.3. These range from 0 (hypergiants) through III (giants) to V (main sequence dwarfs); some authors add VII (white dwarfs). Most stars belong to the main sequence, which consists of ordinary hydrogen-burning stars. These fall along a narrow, diagonal band when graphed according to their absolute magnitude and spectral type. Our Sun is a main sequence G2V yellow dwarf, being of intermediate temperature and ordinary size. Additional nomenclature, in the form of lower-case letters, can follow the spectral type to indicate peculiar features of the spectrum. For example, an "e" can indicate the presence of emission lines; "m" represents unusually strong levels of metals, and "var" can mean variations in the spectral type. White dwarf stars have their own class that begins with the letter D. This is further sub-divided into the classes DA, DB, DC, DO, DZ, and DQ, depending on the types of prominent lines found in the spectrum. This is followed by a numerical value that indicates the temperature index. This is known as the Yerkes spectral classification. Two stars may have the same surface temperature (color) but different luminosity (size), according to their age, mass and composition.

I Supergiant (a/b) II Luminous Giant III GiantIV Subgiant

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V Main Sequence (Dwarf)VI | Subdwarf VII White Dwarf Table 5.3 The major luminosity classes

5.12 Magnitude of Stars (Apparent and Absolute magnitude):

The apparent brightness of a star is measured by its apparent magnitude, which is the brightness of a star with respect to the star’s luminosity, distance from Earth, and the altering of the star’s light as it passes through Earth’s atmosphere. Intrinsic or absolute magnitude is what the apparent magnitude a star would be if the distance between the Earth and the star were 10 parsecs (32.6 light-years), and it is directly related to a star’s luminosity.

Number of stars brighter than magnitude

Apparentmagnitude

Number of Stars

0 4

1 15

2 48

3 171

4 513

5 1,602

6 4,800

7 14,000

Table 5.4 The Luminosity of stars.

Both the apparent and absolute magnitude scales are logarithmic units: one whole number difference in magnitude is equal to a brightness variation of about 2.5 times (the 5th root of 100 or approximately 2.512). This means that a first magnitude (+1.00) star is about 2.5 times brighter than a second magnitude (+2.00) star, and

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approximately 100 times brighter than a sixth magnitude (+6.00) star. The faintest stars visible to the naked eye under good seeing conditions are about magnitude +6.

On apparent and absolute magnitude scales, the smaller the magnitude number, the brighter the star; the larger the magnitude number, the fainter. The brightest stars, on either scale, have negative magnitude numbers. The variation in brightness (ΔL) between two stars is calculated by subtracting the magnitude number of the brighter star (mb) from the magnitude number of the fainter star (mf), then using the difference as an exponent for the base number 2.512; that is to say:

Δm = mf − mb 2.512Δm = ΔL

Relative to both luminosity and distance from Earth, absolute magnitude (M) and apparent magnitude (m) are not equivalent for an individual star; for example, the bright star Sirius has an apparent magnitude of −1.44, but it has an absolute magnitude of +1.41.

The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83. Sirius, the brightest star in the night sky as seen from Earth, is approximately 23 times more luminous than the Sun, while Canopus, the second brightest star in the night sky with an absolute magnitude of −5.53, is approximately 14,000 times more luminous than the Sun. Despite Canopus being vastly more luminous than Sirius, however, Sirius appears brighter than Canopus. This is because Sirius is merely 8.6 light-years from the Earth, while Canopus is much farther away at a distance of 310 light-years.

As of 2006, the star with the highest known absolute magnitude is LBV 1806-20, with a magnitude of −14.2. This star is at least 5,000,000 times more luminous than the Sun. The least luminous stars that are currently known are located in the NGC 6397 cluster. The faintest red dwarfs in the cluster were magnitude 26, while a 28th magnitude white dwarf was also discovered. These faint stars are so dim that their light is as bright as a birthday candle on the Moon when viewed from the Earth.

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5.13 Stellar Diameter

Due to their great distance from the Earth, all stars except the Sun appear to the human eye as shining points in the night sky that twinkle because of the effect of the Earth's atmosphere. The Sun is also a star, but it is close enough to the Earth to appear as a disk instead, and to provide daylight. Other than the Sun, the star with the largest apparent size is R Doradus, with an angular diameter of only 0.057 arcseconds. The disks of most stars are much too small in angular size to be observed with current ground-based optical telescopes, and so interferometer telescopes are required in order to produce images of these objects. Another technique for measuring the angular size of stars is through occultation. By precisely measuring the drop in brightness of a star as it is occulted by the Moon (or the rise in brightness when it reappears), the star's angular diameter can be computed.

Figure 5.5 Stars vary widely in size

Stars range in size from neutron stars, which vary anywhere from 20 to 40 km in diameter, to supergiants like Betelgeuse in the Orion constellation, which has a diameter approximately 650 times larger

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than the Sun—about 0.9 billion kilometers. However, Betelgeuse has a much lower density than the Sun.

5.14 Stellar kinematics

The motion of a star relative to the Sun can provide useful information about the origin and age of a star, as well as the structure and evolution of the surrounding galaxy. The components of motion of a star consist of the radial velocity toward or away from the Sun, and the traverse angular movement, which is called its proper motion. Radial velocity is measured by the Doppler shift of the star's spectral lines, and is given in units of km/s. The proper motion of a star is determined by precise astrometric measurements in units of milli-arc seconds (mas) per year. By determining the parallax of a star, the proper motion can then be converted into units of velocity. Stars with high rates of proper motion are likely to be relatively close to the Sun, making them good candidates for parallax measurements. Once both rates of movement are known, the space velocity of the star relative to the Sun or the galaxy can be computed. Among nearby stars, it has been found that population I stars have generally lower velocities than older, population II stars. The latter have elliptical orbits that are inclined to the plane of the galaxy. Comparison of the kinematics of nearby stars has also led to the identification of stellar associations. These are most likely groups of stars that share a common point of origin in giant molecular clouds.

5.15 Distribution of stars

In addition to isolated stars, there are multi-star system can consisting of two or more gravitationally bound stars that orbit around each other. The most common multi-star system is a binary star, but systems of three or more stars are also found. For reasons of orbital stability, such multi-star systems are often organized into hierarchical sets of co-orbiting binary stars. Larger groups called star clusters also exist. These range from loose stellar associations with only a few stars, up to enormous globular clusters with hundreds of thousands of stars.It has been a long-held assumption that the majority of stars occur in gravitationally bound, multiple-star systems. This is particularly true for very massive O and B class stars, where 80% of the systems are

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believed to be multiple. However the portion of single star systems increases for smaller stars, so that only 25% of red dwarfs are known to have stellar companions. As 85% of all stars are red dwarfs, most stars in the Milky Way are likely single from birth.

Stars are not spread uniformly across the universe, but are normally grouped into galaxies along with interstellar gas and dust. A typical galaxy contains hundreds of billions of stars, and there are more than 100 billion (1011) galaxies in the observable universe. While it is often believed that stars only exist within galaxies, intergalactic stars have been discovered. Astronomers estimate that there are at least 70 sextillion (7×1022) stars in the observable universe.

The nearest star to the Earth, apart from the Sun, is Proxima Centauri, which is 39.9 trillion (1012) kilometers, or 4.2 light-years away. Light from Proxima Centauri takes 4.2 years to reach Earth. Traveling at the orbital speed of the Space Shuttle (5 miles per second—almost 30,000 kilometers per hour), it would take about 150,000 years to get there. Distances like this are typical inside galactic discs, including in the vicinity of the solar system. Stars can be much closer to each other in the centers of galaxies and in globular clusters, or much farther apart in galactic halos.

Due to the relatively vast distances between stars outside the galactic nucleus, collisions between stars are thought to be rare. In denser regions such as the core of globular clusters or the galactic center, collisions can be more common. Such collisions can produce what are known as blue stragglers. These abnormal stars have a higher surface temperature than the other main sequence stars with the same luminosity in the cluster.

5.16 Stellar Structure

The circumstances that greatly facilitate the computation of the conditions in the interior of the stars is that, stars in most cases are completely gaseous throughout. Not only are the temperatures too high to permit the molecules to exist in the stellar interiors but even the atoms almost completely ionized. Consequently, overwhelming majority of particles of which the stars are made are the free electrons and atomic nuclei, and most of the later are simple protons.

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We know that these particles are extremely small as compared to the size of the neutral atoms. Thus even in stars where the gases are compressed to enormous densities, there is mostly empty space between the electrons and atomic nuclei. It is for this reason idealized gas law holds throughout the interior of most of the stars with high degree of accuracy.

(i) Perfect Gas Law: The particles that comprise a gas are in rapid motion, frequently colliding with each other and with the walls of the container of the gas. This constant bombardment is the pressure of the gas. The pressure is greater, the greater the number of particles within a given volume of gas, for the course the combined impact of moving particles increases with the numbers. The pressure is also greater the faster the molecules or atoms are moving; since the rate of motion determined by the temperature of the gas, the pressure is greater the higher the temperature. The perfect gas laws provide the mathematical relation between the pressure density and temperature of a perfect or ideal gas and states that the pressure is proportional to the product of the density and the temperature of the gas. The gases in most stars closely approximate an ideal gas; thus, they must obey this law. The exceptions are very massive stars, where the radiation pressure can play an important role, and collapse core of the stars where the matter is degenerated.

(ii) Hydrostatic Equilibrium:

The sun like majority of other stars is stable that is, neither expanding nor contracting. Such a star is said to be in a condition of equilibrium, all the force within it are balanced so that each point within the star the temperature, pressure and density and so on are maintained at the constant values. However, even these stable stars including the sun, are changing as they evolve, such evolutionary changes are so gradual

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that to all intends and purpose the stars are still in state of equilibrium.

The mutual gravitational attraction between the masses of various regions within a star produces tremendous forces that tend to collapse the star toward its center. Yet, since the star like the sun have remained more or less unchanged for millions of years, the gravitational force that tends to collapse the star must be exactly balanced by a pressure from within. Most of it is the pressure of the gases themselves, although in some very luminous stars the pressure of radiation also contributes appreciably.

If the internal pressure in the star is not great enough to balance the weight of outer parts the star would collapse somewhat, contracting and building up pressure inside. If the pressure were greater than the weight of overlying layers the star would expand, thus decreasing the internal pressure, expansion would stop and the equilibrium would be reached when the pressure at every internal point again equaled the weight of the stellar layers above that point. An analogy is the inflated balloon, which will expand or contract until an equilibrium is reached between the excess pressure of the air and tension of the rubber. This condition is called hydrostatic equilibrium; so are the oceans of the earth; as well as the earth’s atmosphere. The pressure of air keeps the air from falling to the ground.

(iii) Minimum Pressure and Temperature in Stellar Interior

We can regard star as being composed of large number of concentric spherical shells (like the layers of onion). The star is not actually satisfied, of course; we speak of these shells in the same sense that we speak of levels in the ocean. Now if we know how the matter is distributes within the star, that is, what fraction of its

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mass is included within each shell. Since the weight of the shell is the gravitational attraction between it and all the underlying layers, we could then calculate weight of each shell. From the condition of hydrostatic equilibrium, we could next calculate how the pressure must increase downward through each shell to support its weight. At the surface of the star, where there are no overlying layers of stellar matter, the pressure is zero. By simply adding up the increases of pressure through successive layers inward, we would be able to find the pressure at each point within the star, in particular at its center. Using pressure and the densities thus determined at all points along the radius of the star, we could then find the corresponding temperatures from the perfect gas law. In other words if we only know how the material within the star is distributed, we would be able to calculate the density, pressure and temperature at all its internal points. It is not known in advance, how the matter in a particular star is distributed. On the other hand some ways that it is not distributed can be specified. Internal gravity must force the gases comprising the star into higher and higher compression at deeper and deeper levels of its interior. The material is expected to show high central concentrations the density of outer layers would certainly not exceed those of inner layers. To assume that the matter in the star is distributed with uniform density, would certainly be to underestimate its central compression, and the values calculated for its internal pressures and temperatures. Here, then, is a method by which lower limits can be found for pressure and temperature in the stellar interior. With only the assumption of hydrostatic equilibrium and knowledge of perfect gas law it is possible to learn something of conditions in star. We find that the mean pressure in the sun is at least 500 million times the sea-level pressure of earth’s atmosphere; the central pressure is at least 1.3 x 109 times that of earth’s atmosphere, and that the mean temperature is at least 2.3 million Kelvin. Since these pressures and temperatures would exist if

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the sun were uniform in density. The actual values must be much higher, under such conditions all elements are in the gaseous form, and the atoms cannot be combined into molecules. Moreover, most of the atoms are completely ionized, electrons thus freed, from the parent atom become part of gas itself moving about as independent particles.

(iv) Thermal Equilibrium

The observation of stars reveals that electromagnetic energy flow from the surface of the stars. Thus, second law of thermodynamics, heat always tries to flow from hotter to cooler region. Therefore, the energy always filters outwards toward the surface of the star; it must be flowing from inner hotter region. The temperature cannot decrease inward in the star, or energy would flow in and heat up those regions until they were at least as hot as outer ones. Thus we conclude that the highest temperature occurs at the center of the star and that the temperature drops to successively lower values towards the stellar surface. The outward flow of energy though robs of its internal heat and would result in cooling of interior gases where the energy is not replaced. There must therefore be a source of energy within each star.

If the star is in the hydrostatic equilibrium and shining with steady luminosity the temperature and pressure at each point within it must remain approximately constant. If the temperature were to change suddenly at some point, the pressure would similarly change, causing the star to contract suddenly or to expand or otherwise to deviate from the hydrostatic equilibrium. Energy must be supplied therefore, to each layer in the star at just a right rate to balance the loss of heat in that layer as it passes energy outward toward surface. Moreover, the rate at which the energy is supplied to the star as a whole, must at least on the average, exactly balance the rate at which the whole star loses

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its energy by radiating it into space; that is, rate of energy production in a star is equal to its luminosity. We call this balance of heat for the star as a whole and at each point within it the condition of thermal equilibrium.

(v) Heat Transfer in a Star

There are three ways in which teat can be transported; by conduction, by convection and by radiation. The rate at which heat passes through gases by conduction, however, is so low that this mode of transfer can be ignored in stellar interiors, unless the gas is degenerated. The stellar convection occurs as current of gas flow in and out through the star. While these convection currents travel at moderate speed and do not upset the condition of hydrostatic equilibrium, they nevertheless carry heat outward through the star very effectively. The convection current cannot be maintained unless the temperature of successive deeper layers in the star increases rapidly in relation to the rate at which the pressure increases inward. Convection occurs in certain parts of many stars and the convection current may travel completely through some of the least luminous stars.

Unless convection occurs, the only mode of transport of energy through the star is electromagnetic radiation, which gradually filters outward as it is passed from atom to atom. However, the radiative transfer is not an efficient means of energy transport, because under the condition that prevails in the stellar interiors gases are very opaque- that is, a photon do not go far before it is absorbed by an atom(typically in the sun about 1 cm). The energy absorbed by atoms is always reemitted in random directions. A photon that is traveling outward in a star when it is absorbed has almost as good a chance of being radiated back towards the center of the star as towards its surface. A particular quantity of the energy being passed from atom to atom, therefore

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zigzagging around in an almost random manner and take a long time to work its way from the center of the star to its surface, in the sun the time required is of the order of million years.

The measuring the ability of gas to absorb radiation is called its opacity. It should be no surprise that the gases in the sun are opaque. If they were completely transparent then we could see all the way through the sun. The process by which atoms and ions can interrupt the flow of energy - such as by becoming ionized and by bremmstrahlung (free- free transactions). In addition the individual electron can scatter radiation helter-skelter. For a given temperature, density and the compression of a gas, all of these processes can be taken into account, and the opacity can be calculated. Once the opacity is known, we can fins how each layer of shell or the sun or a star impedes the outward flow of radiation. Of course there is such a net outward flow, or the star would have no luminosity. Thus from opacity we calculate how the temperature must increase inward through the shell to force the observed radiation out and thereby learn the temperature distribution throughout the interior. If the temperature difference across some regions of a star should be high enough to support convection, convection currents, rather than radiation carry most of the energy within those regions the variation of temperature are with depth is determined by expansion of outward moving masses of gases and contraction of overlying ones. Here again the knowledge of the energy transport mechanism within a star makes possible calculation of temperature distribution

Thus we can summarize that the interior of a stable star is in a state of hydrostatic equilibrium: the forces on any small volume almost exactly counterbalance each other. The balanced forces are inward gravitational force and an outward force due to the pressure gradient within the star. The pressure gradient is established by the temperature gradient of the plasma; the outer part of the star is cooler

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than the core. The temperature at the core of a main sequence or giant star is at least on the order of 107 K. The resulting temperature and pressure at the hydrogen-burning core of a main sequence star are sufficient for nuclear fusion to occur and for sufficient energy to be produced to prevent further collapse of the star. As atomic nuclei are fused in the core, they emit energy in the form of gamma rays. These photons interact with the surrounding plasma, adding to the thermal energy at the core. Stars on the main sequence convert hydrogen into helium, creating a slowly but steadily increasing proportion of helium in the core. Eventually the helium content becomes predominant and energy production ceases at the core. Instead, for stars of more than 0.4 solar masses, fusion occurs in a slowly expanding shell around the degenerate helium core. In addition to hydrostatic equilibrium, the interior of a stable star will also maintain an energy balance of thermal equilibrium. There is a radial temperature gradient throughout the interior that results in a flux of energy flowing toward the exterior. The outgoing flux of energy leaving any layer within the star will exactly match the incoming flux from below.

The radiation zone is the region within the stellar interior where radiative transfer is sufficiently efficient to maintain the flux of energy. In this region the plasma will not be perturbed and any mass motions will die out. If this is not the case, however, then the plasma becomes unstable and convection will occur, forming a convection zone. This can occur, for example, in regions where very high energy fluxes occur, such as near the core or in areas with high opacity as in the outer envelope. The occurrence of convection in the outer envelope of a main sequence star depends on the mass. Stars with several times the mass of the Sun have a convection zone deep within the interior and a radiative zone in the outer layers. Smaller stars such as the Sun are just the opposite, with the convective zone located in the outer layers. Red dwarf stars with less than 0.4 solar masses are convective throughout, which prevents the accumulation of a helium core. For most stars the convective zones will also vary over time as the star ages and the constitution of the interior is modified. The portion of a star that is visible to an observer is called the photosphere. This is the layer at which the plasma of the star becomes transparent to photons of light. From here, the energy generated at the core becomes free to propagate out into space. It is

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within the photosphere that sun spots, or regions of lower than average temperature, appear.

Above the level of the photosphere is the stellar atmosphere. In a main sequence star such as the Sun, the lowest level of the atmosphere is the thin chromosphere region, where spicules appear and stellar flares begin. This is surrounded by a transition region, where the temperature rapidly increases within a distance of only 100 km. beyond this is the corona, a volume of super-heated plasma that can extend outward to several million kilometers. The existence of a corona appears to be dependent on a convective zone in the outer layers of the star. Despite its high temperature, the corona emits very little light. The corona region of the Sun is normally only visible during a solar eclipse. From the corona, a stellar wind of plasma particles expands outward from the star, propagating until it interacts with the interstellar medium. For the Sun, the influence of its solar wind extends throughout the bubble-shaped region of the heliosphere

Figure 5.6 A cross-section of a solar-type star.

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Summery

1. The total mass of a star is the principal determinant in its evolution and eventual fate.

2. Ancient sky watchers imagined that prominent arrangements of stars formed patterns (constellations), and they associated these with particular aspects of nature or their myths.

3. Most stellar parameters are expressed in SI units by convention, but CGS units are also used (e.g., expressing luminosity in ergs per second). Mass, luminosity, and radii are usually given in solar units, based on the characteristics of the Sun

4. The magnetic field of a star is generated within regions of the interior where convective circulation occurs. The strength of the magnetic field varies with the mass and composition of the star, and the amount of magnetic surface activity depends upon the star's rate of rotation.

5. One of the most massive stars known is Eta Carinae, with 100–150 times as much mass as the Sun; A recent study of the Arches cluster suggests that 150 solar masses is the upper limit for stars in the current era of the universe.

6. Young stars can have a rapid rate of rotation greater than 100 km/s at the equator.

7. Degenerate stars have contracted into a compact mass, resulting in a rapid rate of rotation.

8. The surface temperature of a main sequence star is determined by the rate of energy production at the core and the radius of the star and is often estimated from the star's color index.

9. The energy produced by stars, as a by-product of nuclear fusion, radiates into space as both electromagnetic radiation and particle radiation.

10. The color of a star, as determined by the peak frequency of the visible light, depends on the temperature of the star’s outer layers, including its photosphere.

11. In astronomy, luminosity is the amount of light, and other forms of radiant energy, a star radiates per unit of time.

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12. The stellar spectra differ from each other because of difference in the chemical make up of the star. Actually, the difference in the stellar spectra is due mostly to the widely differing temperatures in the outer layers of the various stars.

13. Stars in the Harvard system are further classified according to their luminosity, a measurement based on the brightness of the star, which gives us some idea of its mass.

14. The apparent brightness of a star is measured by its apparent magnitude, which is the brightness of a star with respect to the star’s luminosity, distance from Earth, and the altering of the star’s light as it passes through Earth’s atmosphere.

15. Due to their great distance from the Earth, all stars except the Sun appear to the human eye as shining points in the night sky that twinkle because of the effect of the Earth's atmosphere.

16. Stars range in size from neutron stars, which vary anywhere from 20 to 40 km in diameter, to supergiants like Betelgeuse in the Orion constellation, which has a diameter approximately 650 times larger than the Sun—about 0.9 billion kilometers.

17. The motion of a star relative to the Sun can provide useful information about the origin and age of a star, as well as the structure and evolution of the surrounding galaxy.

18. In addition to isolated stars, there are multi-star system can consisting of two or more gravitationally bound stars that orbit around each other.

19. Stars are not spread uniformly across the universe, but are normally grouped into galaxies along with interstellar gas and dust. A typical galaxy contains hundreds of billions of stars, and there are more than 100 billion (1011) galaxies in the observable universe.

20. Overwhelming majority of particles of which the stars are made are the free electrons and atomic nuclei, and most of the later are simple protons.

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21. The perfect gas laws provide the mathematical relation between the pressure density and temperature of a perfect or ideal gas and states that the pressure is proportional to the product of the density and the temperature of the gas.

22. There are three ways in which teat can be transported; by conduction, by convection and by radiation.

23. The interior of a stable star is in a state of hydrostatic equilibrium: the forces on any small volume almost exactly counterbalance each other. The balanced forces are inward gravitational force and an outward force due to the pressure gradient within the star. The pressure gradient is established by the temperature gradient of the plasma

Exercises Fill in the blanks

1. Greek astronomer Aristillus created ___________ catalogue in approximately 300 BC.

2. Hipparchus is known for the discovery of the first ________.3. ___________ measurements demonstrated the vast separation

of the stars in the heavens.4. The oldest star yet discovered, HE 1523-0901, is an estimated

________ billion years old.5. Mass, luminosity, and radii are usually given in ________ units.6. Movement of conductive plasma functions like a dynamo,

generating __________ fields that extend throughout the star.7. Massive main sequence stars can have surface temperatures

of _____________K.8. Using the stellar spectrum, astronomers can also determine the

_____________ temperature, surface gravity, metallicity and rotational velocity of a star.

9. Stars in the Harvard system are further classified according to their __________, a measurement based on the brightness of the star.

10. Stars with high rates of proper motion are likely to be relatively close to the _______, making them good candidates for parallax measurements.

11. It has been a long-held assumption that the majority of stars occur in gravitationally bound, __________star systems.

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12. The nearest star to the Earth, apart from the Sun, is Proxima Centauri, which is _________ light-years away.

13. We find that the mean pressure in the sun is at least 500 million times the ___________ pressure of earth’s atmosphere;

14. The three ways in which teat can be transported; by ________, by __________ and by ______________.

Short questions with answer

Q1. When latitudes of various stars obtained?Ans. In the 11th century, Abū Rayhān al-Bīrūnī described the Milky

Way galaxy as multitude of fragments having the properties of nebulous stars, and also gave the latitudes of various stars during a lunar eclipse in 1019.

Q2. Why stars exerted no net gravitational pull on the solar system?Ans. Isaac Newton suggested that the stars were equally distributed

in every direction so that the stars exerted no net gravitational pull on the solar system.

Q3. What is the most useful entity to determine the characteristics of the star?

Ans. Initial Mass is the most important entity used to determine various characteristics of the star. It can be used to determine almost everything about a star, including essential characteristics such as luminosity and size, as well as the star's evolution, lifespan, and eventual fate.

Q4. What is a star?Ans. A star is a massive, luminous ball of plasma that is held

together by gravity.Q5. What is Hertzsprung-Russell diagram?Ans. A Hertzsprung-Russell diagram (H–R diagram) which allows the

age and evolutionary state of a star to be determined is a plot of the temperature of many stars against their luminosities

Q6. What is Binary and multi-star systems?Ans. Binary and multi-star systems consist of two or more stars that

is gravitationally bound, and generally moves around each other in stable orbits.

Q7. What factors influence the magnetic fields of a star?Ans. The strength of the magnetic field varies with the mass and

composition of the star, and the amount of magnetic surface activity depends upon the star's rate of rotation.

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Q8. Name the factors affecting the rate of rotation of a star on a main sequence?

Ans. The star's magnetic field and the stellar wind serve to slow down a main sequence star's rate of rotation by a significant amount as it evolves on the main sequence.

Q9. Which characteristics of the star are used to classify it?Ans. The surface temperature of a star, along with its visual absolute

magnitude and absorption features, is used to classify a star. Q10. What are starspots?Ans. Surface patches with a lower temperature and luminosity than

average are known as starspots.Q11. Why spectrums of the star differ?Ans. The difference in the stellar spectra is due mostly to the widely

differing temperatures in the outer layers of the various stars.Q12. How velocity of a star is determined?Ans. The proper motion of a star is determined by precise

astrometric measurements in units of milli-arc seconds (mas) per year. By determining the parallax of a star, the proper motion can then be converted into units of velocity.

Q13. How stars are structured in the universe?Ans. Stars are not spread uniformly across the universe, but are

normally grouped into galaxies along with interstellar gas and dust.

Q14. Why collisions between stars are thought to be rare?Ans. Due to the relatively vast distances between stars outside the

galactic nucleus, collisions between stars are thought to be rare.

Q115. What is the composition of a star?Ans. Overwhelming majority of particles of which the stars are made

are the free electrons and atomic nuclei, and most of the later are simple protons.

Study QuestionsQ1. What was the belief of ancient astronomers about stars?Q2. What is the significance of the spectrum of a star in determining

its properties?Q3. How stars are designated? What are astronomical naming

conventions?Q4. What is Eddington Luminosity?Q5. How the rotation rate of stars can be approximated?Q6. What is Spectral Sequence?

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Q7. The Sun has an apparent magnitude of −26.7, but its absolute magnitude is only +4.83. Why?

Q8. What are the components of motion of a star?Q9. How stars are distributed in the universe?Q10. Write a note on?

(i) Hydrostatic Equilibrium.(ii) Perfect Gas Law: (iii) Minimum Pressure and Temperature in Stellar Interior.(iv) Thermal Equilibrium.(v) Heat Transfer in a Star.

Q11. Discuss the interior of a stable star?

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Chapter 6Ejnar Hertzsprung (8 October, 1873 - 21

October, 1967) was a Danish chemist and

astronomer. In the period 1911-1913,

together with Henry Norris Russell, he

developed the Hertzsprung-Russell diagram.

Perhaps his greatest contribution to

astronomy was the development of a

classification system for stars to divide them

by spectral type, stage in their development, and luminosity. The so-

called "Hertzsprung-Russell Diagram" was used for many years as a

classification system to explain stellar types and evolution

Henry Norris Russell (October 25, 1877 – February 18, 1957) was an American astronomer who, along with Ejnar Hertzsprung, developed the Hertzsprung–Russell diagram (1910). In 1923, working with Frederick Saunders, he developed Russell–Saunders coupling which is also known as LS coupling.

Stellar EvolutionNo star that is shining today can be infinitely old, for eventually

it will exhaust its source of energy. The stars of highest known luminosity (100 thousand to a million times that of the sun) can continue to exist at the rate they are no expending energy for only a few million years. Had they been formed when the sun was formed, thousands of millions of years ago, they would long since have burned themselves out. At least therefore, some stars have formed

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recently (in astronomical time scale) and there is very reason to expect that the stars are still forming today.

6.1 Hertzsprung-Russell diagram

In 1911 the Danish astronomer E. Hertzsprung compared the colors and luminosity of stars within several clusters by plotting their magnitudes against their colors. In 1913 the American astronomer Henry Norris Russel undertook a similar investigation of stars in the solar neighborhood by plotting absolute magnitudes of stars of known distance against their spectral colors. The investigations by Hertzsprung and by Russell led to an extremely important discovery concerning the relation between the luminosity and the surface temperatures of star. The discovery is exhibited graphically on a diagram named in the honor of two astronomers the Hertzsprung-Russell diagram Figure 6.1

6.2 Features of H-R diagramTo easily derive the characteristics of stars of known distances are their absolute magnitudes (or luminosities) and their surface temperature. The most significant feature of the H-R diagram is that the stars are not distributed over it at random, exhibiting all combinations of absolute magnitude and temperature but rather cluster into certain parts of the diagram. The majority of stars are aligned along a narrow sequence running from upper left (hot highly luminous) part of the diagram to the lower right (cool less luminous) part. This band of points is called main sequence. A substantial number of stars lie above the main sequence of the H-R diagram in the upper right (cool, highly luminous), these are called giants. At the top part of the diagram are the stars of even higher luminosity, called supergiants. Finally, there are stars in the lower left (hot, low luminosity) corner known as white dwarfs. To say that a star lies “on” or “off” the main sequence does not refer to its position in luminosity and temperature on the H-R diagram.

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Figure 6.1 Hertzsprung-Russell diagram for a set of stars that includes the Sun (center).

An H-R diagram, as shown in Figure 6.1 that is, plotted for stars of known distances does not show the relative proportions of various kinds of stars, because only the nearest of the intrinsically joint star can be observed. To be truly representative of stellar population an H-R diagram should be plotted for all stars within certain distance. Unfortunately, our knowledge is reasonable complete only for stars within a few parsecs of the sun, among which there are no giant or supergiants. It is estimated that about 90 percent of the star in our part of the space are main sequence stars and about 10 percent are white dwarfs. Less than 1 percent is giants or supergiants.

6.3 Formation of Star Here and there, in comparatively dense regions of interstellar matter, small condensation begins to form – atoms of gas and particles of dust slowly begin to collect under the influence of their mutual gravitation. The trick, then to forming a star is to arrange for relatively dense cloud of interstellar matter. Most of the gas and the heat in the space are clearly at too low a density to collapse into star or there

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would be no interstellar matter left. Stars are formed within extended regions of higher density in the interstellar medium, although the density is still lower than the inside of an earthly vacuum chamber. These regions are called molecular clouds and consist mostly of hydrogen, with about 23–28% helium and a few percent heavier elements. One example of such a star-forming region is the Orion Nebula. As massive stars are formed from molecular clouds, they powerfully illuminate those clouds. They also ionize the hydrogen, creating an H II region.

How then, do star formed? Several different scenarios by which a protostar condensation may get started are as follows

6.4 Protostar formation (some mechanisms)1. Direct collision of interstellar clouds can cause an increase

of density that could lead to stellar condensations. One way that such collisions can occur is by gas clouds, in a normal galactic rotation encountering density waves of spiral arms. Since the pattern of spiral structures rotates more slowly than the normal galactic rotation, gas clouds should be plowing into the arms along their trailing edges. Consistent with the idea in some other galaxies we see super luminous young stars concentrated along the trailing edges of those galaxies arms.

Figure 6.2 A star forming region in the Large Magellanic Cloud. NASA/ESA image.

2. At the interface between HII regions and in the surrounding HI regions, we expect a buildup of density due to expansion of hot gas in the HII regions (since the hydrogen is the main constituent of the gas we often characterize the region of interstellar space according to whether its hydrogen is

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neutral – an HI region or ionized HII region). The “elephant trunk” intrusions of cooler gas and dust in advancing front of hot HII regions Figure 6.3. A young star cluster NGC2264 appears to have been formed recently in such region.

Figure 6.3 Massier 16 nebula in Serpens.

3. Isolated small clouds of mass estimated at from 20 to several hundred solar masses-globules, an excellent example of a globule is the colasack, a dark region of Milky Way in the direction of Southern Cross Figure 6.4. Astronomer Bart Bok has long called the attention to such globules as probable clouds of gas and dust collapsing into stars or cluster of stars.

Figure 6.4 Fine globule in the southern coalsack the diameter is about a third of a parsec, and the mass is estimated to be 20 solar masses. In the center the absorption by dust of visible light is near 20 magnitudes

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4. Supernova explosions release an enormous amount of energy both in electromagnetic radiation and in the form of violent stellar wind. The energy, like the expanding matter in HII regions, can be effective mechanism for compressing surrounding matter into protostar.

5. Among the most promising sites of star formation are cold molecular clouds. Pare of the energy of the particles in these clouds excites the state of rotation and vibration in the molecules, after which those molecules radiate that energy into the space as infrared and radio waves. In this way, energy is removed from the clouds, which cools it. As it cools, the cloud must contract, until it become gravitationally unstable and becomes a protostar. A well studied clod molecular clouds behind the Orion nebula is believed to be such site.

Figure 6.5 Artist's conception of the birth of a star within a dense molecular cloud. NASA image

Once the stellar condensation starts probability that contracting cloud has at least some rotation, it is for no other reason that it is formed from the material undergoing the differential rotation in the galaxy, Early on , the rotation is likely to be exceedingly slow, but to conserve the angular momentum the cloud must spin faster an faster as it contract. The angular momentum in fact, will probably prevent the clouds collapsing entirely to a single star. In the solar system, the

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nebula flattened to a disk, and the planets accreted in the disk. Today, the planets posses 98 percent of the angular momentum of the entire system. The formation of planets may be a common place, but often, at least the cloud must split and form two or more stars, whose orbital motion about each other contain most of the angular momentum. It may be that formation of planetary system or a multiple star systems are two alternatives open to a condensing cloud.

The formation of a star begins with a gravitational instability inside a molecular cloud, often triggered by shock waves from supernovae (massive stellar explosions) or the collision of two galaxies (as in a starburst galaxy). Once a region reaches a sufficient density of matter to satisfy the criteria for Jeans Instability it begins to collapse under its own gravitational force.

The Jeans Instability occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium such that

Where Menc is the enclosed mass, p is the pressure, ρ is the density of the gas, G is the gravitational constant and r is the radius. T)

6.5 Young StarThe evolution of a stellar condensation after it has solved the problem of angular momentum moves on the path of becoming a normal star. As its matter contracts, its density increases until eventually it become opaque to electromagnetic radiation. The very contraction, however, releases gravitational potential energy and when the protostar become opaque, all of that energy cannot be radiated away. And some become trapped. This heats the interior of star and raises the internal pressure. When those pressures become high enough to support the weights of outer material that has been falling inward, hydrostatic equilibrium is reached. Calculations by R. B. Larson show that equilibrium is reached in the central region first, while the matter from the outer parts of nebula is still falling in, compressing heating and joining the condensed core. When the protostellar cloud has approximately reached the stable condition of hydrostatic equilibrium,

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a protostar forms at the core. Thus, a stellar embryo forms inside, which is surrounded by a collapsing envelop that has not yet come to hydrostatic equilibrium. At least in some stars dust should condense in that envelope, which may completely hide a star in visible light. However, the energy radiated from the hot embryo and then absorbed by the dusty envelope must be reradiated at wavelengths characteristics of lower temperature of the envelope, that is, in infrared. For this reason, observational search for extremely young stars are made at infrared wavelengths.

A young star itself is not yet self-sustaining with nuclear reactions but drives its energy from the gravitational contraction. The period of gravitational contraction lasts for about 10–15 million years. As the radiation filters out through the opaque star and is eventually radiatedinto the space. The internal temperature and the pressure would drop, upsetting the hydrostatic equilibrium, unless the star contracts slightly. Half of the energy released by contraction escapes as radiation , contributing to the stars luminosity , while the other half heats the interior, continually building up the internal pressure to support the increased weights of layers in the star – the weight of each shell of material is inversely proportional to the square of the radius of the shell.

In theoretical study of stellar evolution, we compare a series of models for a star each successive model representing a later point in time. Given one model, we can calculate how the star should change (in the case of young star currently under discussion, due to gravitational contraction), and hence what the star will be like at a slight later time. At each step we find the luminosity and the radius of the star and from these its surface temperature and we can find where the star (or its embryo) should be represented on Herhzsprung - Russel diagram. We thus follow the theoretical evolution of the star from it’s calculate track on H-R diagram.

In the early contraction phase, star transports its internal energy by convection currents. The Japanese astrophysicist C Hayashi first showed that such star must lie in a zone on H-R diagram extending nearly vertically from the lower main sequence to the right extreme of the regions occupied by red supergiants (shaded region Figure 6.6) There can be no stable star such that the point representing it on H-R

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diagram lies to the right of this zone. In accordance with Hayashi theory, stars in the initial stage of their evolution contract and move downward (on H-R diagram) in a zone along Hayashi line. Representative tracks for stars or stellar embryos of several masses and of chemical composition more or less like the sun‘s are shown in Figure 6.6.

Figure 6.6 Theoretical evolutionary track of contracting stars or stellar embryos on Hertzsprung-Russell diagram. According to the calculations by Larson, stars or embryos lying roughly above the dashed line are still surrounded by infalling matter and would be hidden by it.

With the exception for stars of low masses, after the period of some thousands or millions of years, the convection current ceases at the center of the star, and the energy must be transported by radiation in those regions. The central zone in radiative equilibrium gradually grows in size, while the convection current extends less and less deeply beneath the stellar surface. In this stage of stellar evolution, the star or its embryo, still slowly shrinking and deriving its energy from gravitational contraction, turns sharply on the H-R diagram and moves left almost horizontally, towards the main sequence. Eventually, as the release of gravitational energy continues to heat up the star’s interior, its central temperature become high enough to support the nuclear reactions. Soon this new source of energy supplies heat to the interior of the star as fast as the energy is radiated away. The central pressures and temperatures are thus maintained and the contraction of star ceases; it is now on the main

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sequences by this time the in falling of the material is complete and the star is fully formed. A small on the evolutionary tracks of the stars, shown in Figure 6.6, just before they reach the main sequence are the points (according to theory) where the onset of nuclear-energy release occurs. Calculations by Larson show that the stars more massive than the sun would not be visible to us during most of their pre-main sequence evolution because the light they emit is absorbed by the surrounding dust in the in falling material.

By the time the stars of mass appreciably greater than the sun’s have reached the main sequence, the outer convection zone has disappeared, but new cores of convection exist at their centers. Main sequence stars of mass near that of the sun still have appreciable regions in their outer layers in convection, with their deep interiors in radiative equilibrium and follow the Hayashi lines right down to the main sequence, where nuclear reactions finally stops their contraction. Stars of extremely low mass, on the other hand, never achieve high enough central temperature to ignite the nuclear reactions They continues to contract until ( after an extremely long time) they are so dense that their matter become degenerate, and they reach white dwarf stage, the lower end of the main sequence is considered to be that point at which star have a mass just barely great enough to sustain nuclear reaction at sufficient rate to stop gravitational contraction; this critical mass is calculated to be near 1/12 that of the sun. Early stars of less than 2 solar masses are called T Tauri stars, while those with greater mass are Herbig Ae/Be stars. These newly born stars emit jets of gas along their axis of rotation, producing small patches of nebulosity known as Herbig-Haro objects.

At the other extreme the upper end of main sequence terminates at the point where the mass of the star would be so high and the internal temperature so great that the radiation pressure would dominate. The radiation produced from nuclear reactions would be so extreme that when absorbed by the stellar material it would impart to it a force greater than that produced by the gravitation; hence, such a star could not be stable. The upper limit to stellar mass is calculated to be in the range 60 to 100 solar masses.

In general, the pre main sequence evolution of a star down with time; the numbers labeling the points on each evolution track in

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Figure 6.6 are the times in years, required for the embryo star to reach those stages of contraction. The time for whole evolutionary process is highly mass dependent. Stars of mass much higher than the sun’s reach the main sequence in few thousands to a million years; the sun requires millions of years; tens of millions of years are required for stars to evolve to the lower main sequence. For stars three evolutionary time scales are distinguished.

1. The initial gravitational collapse from interstellar matter is relatively quick once the condensation is; say 1000 AU in diameter, the time for it to reach the hydrostatic equilibrium is measured in thousands of years.

2. Pre main sequence gravitational contraction is much more gradual, from onset of hydrostatic equilibrium to the main sequence requires, typically, millions of years.

3. Subsequent evolution on the main sequence is very slow, for a star changes only as thermonuclear reactions alter its chemical composition. For a star of a solar mass, this gradual process requires thousands of millions of years. All evolutionary stages are relatively faster in stars of high mass and slow in those of low mass.

6.6 Evolution from The Main sequence to Giants As soon as the star has reached the main sequence, it derives its energy almost entirely from the thermonuclear conversion of hydrogen to helium. Stars spend about 90% of their lifetime fusing hydrogen to produce helium in high-temperature and high-pressure reactions near the core. Here only 0.7 percent hydrogen used up is converted to energy, the star does not change its mass appreciably, but in its central regions, where the nuclear reaction occur, the chemical composition gradually changes as hydrogen is depleted and helium is accumulated there. This change of composition forces the star to change its structure, including its luminosity and size. Eventually the point that represents it on H-R diagram evolves away from the main sequence. The original main sequence, corresponding to stars of homogeneous chemical composition, is called zero age main sequence. Starting at zero-age main sequence, the proportion of helium in a star's core will steadily increase. As a consequence, in order to maintain the required rate of nuclear fusion at the core, the

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star will slowly increase in temperature and luminosity. The Sun, for example, is estimated to have increased in luminosity by about 40% since it reached the main sequence 4.6 billion years ago. Every star generates a stellar wind of particles that causes a continual outflow of gas into space. For most stars, the amount of mass lost is negligible. The Sun loses 10−14 solar masses every year, or about 0.01% of its total mass over its entire lifespan. However, very massive stars can lose 10−7 to 10−5 solar masses each year, significantly affecting their evolution. Stars that begin with more than 50 solar masses can lose over half their total mass while they remain on the main sequence.

6.7 Evolution from The Main sequence to Giants

As helium accumulate at the expense of hydrogen in the center of the star, the temperature and the density increases in the region. Consequently the rate of nuclear energy generation increases and the luminosity of the star slowly rise. A star, therefore does not remain indefinitely exactly on the zero-age main sequence. In fact, the main sequence of a star cluster gradually rises in H-R diagram as cluster ages. The most massive and luminous stars alter their chemical composition most quickly, thus the main sequence rises more rapidly at the bright end, but scarcely not all at the faint end, even after billions of years. This stage of evolution does not cause the main sequence of a star cluster to deform appreciably, because the star increases its luminosity only by small amount-probably less than a magnitude before subsequent more rapid changes alter its structure enormously.

When the hydrogen has been depleted completely in the central part of the star, a core develops containing helium “contaminated” by whatever small percentages of heaver elements the star has to begin with. The duration that a star spends on the main sequence depends primarily on the amount of fuel it has to fuse and the rate at which it fuses that fuel. In other words, it’s initial mass and its luminosity. For the Sun, this is estimated to be about 1010 years. Large stars consume their fuel very rapidly and are short-lived. Small stars (called red dwarfs) consume their fuel very slowly and last tens to hundreds of billions of years. At the end of their lives, they simply become dimmer and dimmer. However, since the lifespan of such stars is greater than the current age of the universe (13.7 billion years), no

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such stars are expected to exist yet. Besides mass, the portion of elements heavier than helium can play a significant role in the evolution of stars. In astronomy all elements heavier than helium are considered a "metal", and the chemical concentration of these elements is called the metallicity. The metallicity can influence the duration that a star will burn its fuel, control the formation of magnetic fields and modify the strength of the stellar wind. Older, population II stars have substantially less metallicity than the younger, population I stars due to the composition of the molecular clouds from which they formed. (Over time these clouds become increasingly enriched in heavier elements as older stars die and shed portions of their atmospheres.)

When the energy source from hydrogen burning is now used up and with nothing more to supply heat to the helium core, it begins again to contract gravitationally. Once more the star’s energy is partially supplied by the potential energy released from contracting core; the rest of its energy comes from hydrogen burning in the region immediately surrounding the core. These changes result in a substantial and rather rapid readjustment of the star’s entire structure, so that the star leaves the vicinity of the main sequence altogether. About ten percent of a star’s mass must be depleted of hydrogen before the star evolves away from the main sequence. The more luminous and a massive star, and sooner this happen, ending its term on the main sequence. Because total rate of energy production in a star must be equal to its luminosity, the core hydrogen is used up first in the very luminous stars. The massive stars spend less than1 million years on the main sequence; a star of one solar mass remain there for 1010 years and a spectral type M0V star of about 0,4 solar mass has the main sequence life of 2 x 1011 years.

6.8 Evolution to Red Giants

As the core contracts it releases gravitational potential energy, which is absorbed in surrounding envelope, these by forcing the outer parts of star to distend greatly. The star as a whole, therefore, expands to enormous proportions; all but its central parts acquire a very low density. The expansion of the outer layers causes them to cool and the star become red. Meanwhile, some of the potential energy released from the contracting core heats up the hydrogen

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surrounding it to even higher temperatures. In these hot regions the conversion of hydrogen to helium accelerates, causing most actually to increase its total luminosity. After leaving the main sequence, then, stars move to upper right portion of the H-R diagram; they become red giants. As shown in Figure 6.7 which is based on theoretical calculations by Illinois astronomer Icko Iben, shows the tracks of evolution on the H-R diagram from the main sequence to the red giants for the stars of several representative masses and with chemical composition similar to that of the sun. Broad band is the zero-age main sequence. The numbers along the tracks indicates the times, in years required for the stars to reach those points on their evolution after leaving the main sequence.

Figure 6.7 Predicted evolutions of the stars from the main sequence to red giants.

6.9 Final Stage of Evolution: Death of an old Star

After the star has become the redgiant the core of the star is shrinking while the outer envelope extends. Gravitational energy released in the contracting core heats it, until by the time a star releases top of the red giant branch on H-R diagram its central temperature exceeds 100 million Kelvin. At such high temperature, nuclear process other than carbon cycle and proton-proton chain are

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possible. The most important of these is the formation of a carbon nucleus by three helium nuclei (the triple alpha process- so named because the nucleus of helium atom is called an alpha particle). Successive bombardment of a carbon nucleus by helium nuclei can build up other still heavier nuclei. The astrophysicist G. Burbidge, E. Burbidge, W. Fowler and F. Hoyle have found the mechanism whereby virtually all the chemical elements upto iron can be synthesized in the center of the red giant stars, in approximately the relative abundances with which they occur in nature. It now seems quite possible that a gradual buildup of elements heavier than helium is continually going on in the hot centers of at lease more massive red giants. The triple alpha process is expected to begin abruptly in the central core of red giant. As the core evolves, not only does it get very hot but also very dense, and the number of inner most part becomes electron degenerate. Meanwhile the surrounding matter soon exhausts all its hydrogen and also contracts until it become electron degenerate and join the core. With its increased mass and consequent release of gravitational energy, core becomes smaller and nondegenerate nuclei become hotter. Thus the degenerate core continues to contract and heat. As soon as the temperature become high enough to start triple alpha process going, the extra energy released is transmitted quickly through the entire degenerate core, producing a rapid heating of all helium there. With the sudden rise in temperature, helium burning accelerates; the phenomenon is called helium flash.

New energy released removes the degeneracy, expands the core, and reverse the growth of outer parts of red giant. The star then shrinks rapidly and increase surface temperature. Calculations indicates that the points representing a star on H-R diagram takes on a new position either to the left of its place as a red giant or somewhat below it. Usually a newly formed carbon nucleus is joined by another helium nucleus to produce the nucleus of oxygen. As soon as the helium is exhausted in the central region, the energy release from triple alpha process is over, and we have the situation analogous to that of a main-sequence star when its central hydrogen is used up, and hydrogen burning ceases in its center. Now we have the core of carbon and oxygen (and perhaps heavier elements) surrounded by a shell where helium is still burning; further out in the star is another shell where hydrogen is left and still burning. The star

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now moves on H-R diagram back to red giant domain, calculations indicates that a star may actually first to the left across the H-R diagram, and then back to be a red giant several times, each time as consequence of onset of new nuclear reactions or of nuclear energy released in new parts of the star. All these evolutionary stages occur in tens or hundreds of millions of years or less-a brief time compared with the star’s main-sequence lives. Some observational evidences supporting the theoretical calculations in the presence of horizontal branch of star on H-R diagram of globular clusters and possibly some open clusters.

Figure 6.8 Betelgeuse is a red supergiant star approaching the end of its life cycle

Thus during their helium-burning phase, very high mass stars with more than nine solar masses expand to form red supergiants. Once this fuel is exhausted at the core, they can continue to fuse elements heavier than helium. The core contracts until the temperature and pressure are sufficient to fuse carbon. This process continues, with the successive stages being fueled by neon, oxygen, and silicon. Near the end of the star's life, fusion can occur along a series of onion-layer shells within the star. Each shell fuses a different element, with the outermost shell fusing hydrogen; the next shell fusing helium, and so forth. The final stage is reached when the star begins producing iron. Since iron nuclei are more tightly bound than any heavier nuclei, if they are fused they do not release energy—the process would, on the contrary, consume energy. Likewise, since they are more tightly bound than all lighter nuclei, energy cannot be released by fission. In relatively old, very massive stars, a large core of inert iron will accumulate in the center of the star. The heavier

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elements in these stars can work their way up to the surface, forming evolved objects known as Wolf-Rayet stars that have a dense stellar wind which sheds the outer atmosphere.

6.10 Chemical composition or Metallicity

When stars form in the present Milky Way galaxy they are composed of about 71% hydrogen and 27% helium, as measured by mass, with a small fraction of heavier elements. Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere, as iron is a common element and its absorption lines are relatively easy to measure. Because the molecular clouds where stars form are steadily enriched by heavier elements from supernovae explosions, a measurement of the chemical composition of a star can be used to infer its age. The portion of heavier elements may also be an indicator of the likelihood that the star has a planetary system. The star with the lowest iron content ever measured is the dwarf HE1327-2326, with only 1/200,000th the iron content of the Sun. By contrast, the super-metal-rich star μ Leonis has nearly double the abundance of iron as the Sun, while the planet-bearing star 14 Herculis has nearly triple the iron. There also exist chemically peculiar stars that show unusual abundances of certain elements in their spectrum; especially chromium and rare earth elements.

6.11 Stellar Nucleosynthesis

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition, as part of stellar nucleosynthesis. The net mass of the fused atomic nuclei is smaller than the sum of the constituents. This lost mass is released as electromagnetic energy, according to the mass-energy equivalence relationship E = mc².The hydrogen fusion process is temperature-sensitive, so a moderate increase in the core temperature will result in a significant increase in the fusion rate.

As a result the core temperature of main sequence stars only varies from 4 million K for a small M-class star to 40 million K for a massive O-class star. In the Sun, with a 10 million K core, hydrogen fuses to form helium in the proton-proton chain reaction:

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41H → 22H + 2e+ + 2νe (4.0 MeV + 1.0 MeV)21H + 22H → 23He + 2γ (5.5 MeV)23He → 4He + 21H (12.9 MeV)

These reactions result in the overall reaction:

41H → 4He + 2e+ + 2γ + 2νe (26.7 MeV)

Where e+ is a positron, γ is a gamma ray photon, νe is a neutrino, and H and He are isotopes of hydrogen and helium, respectively.

The energy released by this reaction is in millions of electron volts, which is actually only a tiny amount of energy. However enormous numbers of these reactions occur constantly, producing all the energy necessary to sustain the star's radiation output.

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon—the carbon-nitrogen-oxygen cycle. In evolved stars with cores at 100 million K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:

Element Solar masses

Hydrogen 0.01

Helium 0.4

Carbon 5

Neon 8Table 6.1 Minimum stellar mass required for fusion

4He + 4He + 92 keV → 8*Be 4He + 8*Be + 67 keV → 12*C 12*C → 12C + γ + 7.4 MeV

For an overall reaction of:

34He → 12C + γ + 7.2 MeV

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In massive stars, heavier elements can also be burned in a contracting core through the neon burning process and oxygen burning process. The final stage in the stellar nucleosynthesis process is the silicon burning process that results in the production of the stable isotope iron-56. Fusion can not proceed any further except through an endothermic process, and so further energy can only be produced through gravitational collapse. The example below shows the amount of time required for a star of 20 solar masses to consume all of its nuclear fuel. As an O-class main sequence star, it would be 8 times the solar radius and 62,000 times the Sun's luminosity.

Fuel materialTemperature

(million kelvins)Density(kg/cm³)

Burningduration(τ in years)

H 37 0.0045 8.1 million

He 188 0.97 1.2 million

C 870 170 976

Ne 1,570 3,100 0.6

O 1,980 5,550 1.25

S/Si 3,340 33,400 0.0315 Table 6.2 Burning time of a star Nuclear fusion reaction pathways

Figure 6.9 Overview of the proton-proton chain

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Figure 6.10 The carbon-nitrogen-oxygen cycle

I.11 Variable Stars

Most of the stars shine with constant light. A minority, however are variable in magnitude. The standard International Index of stars that vary in light is Soviet General Catalogue of variable stars. The 1968 edition of this catalogue lists 20448 known variable stars in our Galaxy, but supplements of this catalogue increase the number yearly.

I. Designation The variable stars are designated in order of the time of discovery in the constellation in which they occur. If the star that is discovered to vary in light already has the proper name or a Greek letter designation, it retains that name; examples are Polaris, Betelgeuse (or α Orion), Algol and δ

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Cephide, otherwise the first star to be recognized as a variable in a constellation is designated by capital letter R followed by possessive of the Latin name of the constellation. For example, R Coronae Borealis. Subsequently discovered variables in the same constellation are designated with the letters S, T, -------Z,

Figure 6.11 The asymmetrical appearance of Mira, an oscillating variable star. NASA HST image

RR, RS-------RZ, SS, ST --------SZ and so on until ZZ is reached. Then the letters AA.AB, ----AZ, BB, BC-------BZ and so on used upto QZ except that the letter J is omitted. This designation takes care of first 334 variable stars in any one constellation. Thereafter the letter V followed by number is used beginning with V335 examples are V335 Hercules and V335 Ophiuchi.

II. Light Curve A variable star is studied by analyzing its spectrum and by measuring the variation of its light with lapse of time. Some stars show the light variation that is apparent to the unaided eye. Generally the apparent brightness of a

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variable star is determined by the telescope observation. The three techniques most commonly employed are as following:

a. The magnitude of the variable is estimated by visual observation through the telescope, by comparing its brightness of neighboring star of known magnitude.

b. The magnitude of the variable star is measured by comparing its image with the image of comparing star on a telescope.

c. The magnitude of the variable is determined by photoelectric photometry.

A graph that shows how the magnitude of a variable star changes with time is called Light Curve of a star. As shown in Figure 6.12. The maximum is the point on the light curve where the maximum amount of light is received from the star; the minimum is the point where the least amount of light is received. If the light variation of variable star repeats themselves periodically, the interval between the successive maxima is called period of a star. The median light of a variable star is amount of light it emits when it is halfway between maxima and minima. The amplitude is the difference between maxima and minima. The amplitudes of variable stars range from less than 0.1 to several magnitudes.

Figure 6.12 Light curve of typical Cepheid variable.

III. Types of variable Stars

The general catalogue of variable stars lists three types of variable stars

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(a) Pulsating Variables These are the stars that periodically expand and contract, pulsating in size as well as in light. That is, pulsating variable stars vary in radius and luminosity over time, expanding and contracting with periods ranging from minutes to years, depending on the size of the star. This category includes Cepheid and Cepheid-like stars, and long-period variables such as Mira.

(b) Eruptive Variables In these stars the sudden, unusual unpredictable outburst of light or in some cases, diminutions of light is seen, that is, eruptive variables are stars that experience sudden increases in luminosity because of flares or mass ejection events. This group includes protostars, Wolf-Rayet stars, and Flare stars, as well as giant and supergiant stars.

(c) Eclipsing Variables They are also called eclipsing binary stars. These are two stars whose orbit of mutual revolution lies nearly edge on to our line of sight and which periodically eclipse each other. Eclipsing variables are not, of course true variable stars. The catalogue numbers of different kinds of variable stars (in 1968) is summarized in Table 6.3 24.3

(d) Long period Variables The largest group pulsating star consists of Mira-type stars; these are named after their prototype, Mira in the constellation of Cetus other large group pulsating stars are RR Lyrae variables; the semiregular variables and the irregular variables. The Mira or red variables are giant stars that pulsate in very long or somewhat irregular periods of months or years. Because they are not highly predictable, an important service provided by amateur astronomers who keep track of the magnitudes of these stars.

(e) Cepheid Variables This is relatively large and important group in astronomy, they are large yellow stars named for proto type and first known star of group δ Cepheid. The magnitude of δ Cepheid varies between 3,6 to 4.3 in period of 5.4 days Figure 6.12.More than 700 Cepheids variables

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are known in our Galaxy. Most Cepheids have period in the range 3 to 50 days and absolute magnitude from -1.5 to -5.

(f) RR Lyrae Next to long term variables, the most common variable stars are RR Lyrae stars; named for RR Lyrae. They are approximately 4500 in our Galaxy. Almost all of them are found in the nucleus of our Galaxy. They have the period of less than a day it is in the range 0.3 to 0.7 days. Their amplitude never exceeds two magnitude and most stars have magnitude less than one.

Type NumberPulsating 13,782Eruptive 1,618Eclipsing 4,062

Unclassified or unstudied 986All Kinds 20,448

Table 6.3 Number of Variable Stars

6.13 Binary Stars Roughly half the stars around the sun are found in pairs (binary stars) or in a system of three or more, ranging upto cluster of thousands each star moving under the combined gravitational influence of other.

6.14 Discovery of Binary Stars In 1650 the Italian Jesuit astronomer Giovanni Baptista Riccioli observed that the star Mizar in the middle of the handle of the Big Dipper appeared through his telescope as two stars. Mizar was first double star to be discovered. In the century and half that followed, many other closely separated pairs of stars were discovered telescopically. One famous double star is Castor in Gemini They are separated by an angle of nearly 5” in 1804, when Herschel had noted that the fainter component of Castor and changed, slightly its direction from the brighter component. Here, finally was observational evidence that one star was moving about another; it was first evidence that the gravitational influences exists outside the solar system. Catalogue prepared by John Herschel contain more than 10,000 systems of two, three or more stars.

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If the gravitational force between the stars is like those in the solar system, the orbit of one star about the other must be an ellipse. Evidence in this regard was found by Felix Savary in 1827 who showed that relative orbits of the two stars in double system ξ Ursae Majoris is an ellipse, the stars completing one mutual revolution in a period of 80 years. Binary stars are now known to be very common; they may be the rule, not the exception, In the stellar neighborhood of the sun somewhere between one half and two third of all the stars are members of binary or multiple star system, Different types of binary star systems can be summarized as follows:

I. Optical Doubles These are two stars in nearly same line of sight, which one is far more distant than the other, they are not they are not true binary stars, and are not discussed further.

II. Visual Binaries These are gravitationally associated pairs of stars; the members are either so near the sun or so widely separated from each other (usually, both) that they can be observed visually (in the telescope) as two stars. The typical separations for the two stars in the visual binary system are hundreds of AU. Thus the orbital speeds of stars are usually quite small and their orbital motion may not be apparent over the few decades of observation. Nevertheless, two closely separated stars are generally assumed to comprise a visual binary system if there is no reason to doubt that they are at the same distance from us and if they have the same proper motion and radial velocity, indicating that they are moving together through space. Over 64,000 such systems are catalogued.

III. Astrometric Binaries Sometimes one member of what would otherwise be a visual binary system is to faint to be observed; its presence may be detected, however, by the “wavy “ motion of its companion, revolving about the invisible center of mass of the two stars as they move through the space. In 1844, Bessel discovered that the bright star Sirius; display such a motion with a period of 50 years. Sirius remained an astrometric binary until 1862, when Alvan G. Clark found its companion- a member of the class of stars known as white dwarfs.

IV. Spectroscopic Binaries When the binary nature of the star is known only from the variations of its radial velocity (or of both radial velocities if the spectral lines of both stars are visible), it is said to

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be spectroscopic binary. Over 700 such systems have been analyzed.

V. Spectrum Binaries If the orbit of what would otherwise be a spectroscopic binary is oriented nearly “face On” to us (that is, perpendicular to our line of sight), or if the masses of the member stars are so low that they have very small orbital velocities, we can see no radial-velocity variations. It may still be obvious, that they are two stars if the composite spectrum contains lines that are the characteristic of both hot and cold stars and which would not be expected to occur in the spectrum of a single star, such system is called spectrum binaries.

VI. Eclipsing Binaries If the orbit of the binary system is oriented nearly edge on to us so that the stars eclipse each other, it is called eclipsing binary. More than 4000 such systems are catalogued.

The different kinds of binaries are not mutually exclusive All eclipsing binary, for example, may also be spectroscopic binary, if I is bright enough that its spectrum can be photographed, and if its radial velocity variations have been observed. Also a small number of relatively nearby spectroscopic binaries can also be observed as visual binaries. Figure 6.13, 6.14 shows the mutual revolution of K60.

Figure 6.13 Photographs of showing the mutual revolution of the components of double star Kuger 60

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Figure 6.14 The mutual revolution during the period 12 years of the revolution of components of double star Kuger 60.

Summery

1. The most significant feature of the H-R diagram is that the stars are not distributed over it at random, exhibiting all combinations of absolute magnitude and temperature but rather cluster into certain parts of the diagram.

2. About 90 percent of the star in our part of the space is main sequence stars and about 10 percent are white dwarfs. Less than 1 percent is giants or supergiants.

3. Stars are formed within extended regions of higher density in the interstellar medium, although the density is still lower than the inside of an earthly vacuum chamber.

4. Several different scenarios by which a protostar condensation may get

5. Several different scenarios by which a protostar condensation may get started are as follows

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6. Direct collision of interstellar clouds can cause an increase of density that could lead to stellar condensations

7. At the interface between HII regions and in the surrounding HI regions,

8. Isolated small clouds of mass estimated at from 20 to several hundred solar masses-globules,

9. Supernova explosions release an enormous amount of energy both in electromagnetic radiation and in the form of violent stellar wind.

10. Among the most promising sites of star formation are cold molecular clouds.

11. It may be that formation of planetary system or a multiple star systems are two alternatives open to a condensing cloud

12. The upper limit to stellar mass is calculated to be in the range 60 to 100 solar masses

13. The time for whole evolutionary process is highly mass dependent.

14. The most massive and luminous stars alter their chemical composition most quickly, thus the main sequence rises more rapidly at the bright end, but scarcely not all at the faint end, even after billions of years

15. In astronomy all elements heavier than helium are considered a "metal", and the chemical concentration of these elements is called the metallicity

16. The metallicity can influence the duration that a star will burn its fuel, control the formation of magnetic fields and modify the strength of the stellar wind

17. It now seems quite possible that a gradual buildup of elements heavier than helium is continually going on in the hot centers of at lease more massive red giants.

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18. The sudden rise in temperature, helium burning accelerates; the phenomenon is called helium flash.

19. Stars form in the present Milky Way galaxy they are composed of about 71% hydrogen and 27% helium, as measured by mass, with a small fraction of heavier elements.

20. A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition, as part of stellar nucleosynthesis.

21. The net mass of the fused atomic nuclei is smaller than the sum of the constituents.

22. The variable stars are designated in order of the time of discovery in the constellation in which they occur.

23. A variable star is studied by analyzing its spectrum and by measuring the variation of its light with lapse of time.

24. The median light of a variable star is amount of light it emits when it is halfway between maxima and minima.

Exercises Fill in the blanks

1. A substantial number of stars lie above the main sequence of the H-R diagram in the upper right (cool, highly luminous), these are called ___________.

2. Stars in the lower left (hot, low luminosity) corner known as ___________.

3. To be truly representative of stellar population a ____________should be plotted for all stars within certain distance.

4. Stars are formed within extended regions of ______________ in the interstellar medium.

5. Supernova ___________ release an enormous amount of energy both in electromagnetic radiation and in the form of violent stellar wind.

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6. The formation of a star begins with_____________ instability inside a molecular cloud.

7. The evolution of a stellar condensation after it has solved the problem of _______________ moves on the path of becoming a normal star.

8. The stars more massive than ________ would not be visible to us during most of their pre-main sequence evolution because the light they emit is absorbed by the surrounding dust in the in falling material.

9. The original _______________, corresponding to stars of homogeneous chemical composition, is called zero age main sequence.

10. A graph that shows how the magnitude of a variable star changes with time is called ______________ of a star.

Short questions with answer

Q1. What relation did the study by Hertzsprung and by Russell led to?

Ans. The investigations by Hertzsprung and by Russell led to an extremely important discovery concerning the relation between the luminosity and the surface temperatures of star.

Q2. How stars are aligned on Hertzsprung - Russell diagram?

Ans. The majority of stars are aligned along a narrow sequence

running from upper left (hot highly luminous) part of the diagram

to the lower right (cool less luminous) part. This band of points

is called main sequence. A substantial number of stars lie

above the main sequence of the H-R diagram in the upper right

(cool, highly luminous), these are called giants. At the top part

of the diagram are the stars of even higher luminosity, called

supergiants. Finally, there are stars in the lower left (hot, low

luminosity) corner known as white dwarfs.Q3. What are the different scenarios by which a protostar

condensation may get started?Ans. Several different scenarios by which a protostar condensation

may get started are as follows

Direct collision of interstellar clouds

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At the interface between HII regions and in the surrounding

HI regions

Isolated small clouds of mass estimated at from 20 to

several hundred solar masses

Supernova explosionsQ4. What are the most promising sites of star formation?Ans. Among the most promising sites of star formation are cold

molecular clouds.Q5. What are the alternatives open to a condensing cloud for the

formation of star?Ans. That formation of planetary system or a multiple star systems

are two alternatives open to a condensing cloud. Q6. What is Jeans Instability?Ans. It is an instability which occurs when the internal gas

pressure is not strong enough to prevent gravitational collapse of a region filled with matter. Thus it begins to collapse under its own gravitational force.

Q7. What are the factors that influence the evolution of a star?Ans. Mass and the portion of elements heavier than helium can play

a significant role in the evolution of stars.Q8. What are metals in astronomy? What is the effect of metallicity

on stellar evolution?

Ans. In astronomy all elements heavier than helium are considered a

"metal", and the chemical concentration of these elements is

called the metallicity. The metallicity can influence the duration

that a star will burn its fuel, control the formation of magnetic

fields and modify the strength of the stellar windQ9. What is the main sequence lifetime of different stars?

Ans. The massive stars spend less than1 million years on the main

sequence; a star of one solar mass remain there for 1010 years

and a spectral type M0V star of about 0,4 solar mass has the

main sequence life of 2 x 1011 years.Q10. What is the helium flash? When does it occur?Ans. As soon as the temperature become high enough to start triple

alpha process going, the extra energy released is transmitted

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quickly through the entire degenerate core, producing a rapid heating of all helium there. With the sudden rise in temperature, helium burning accelerates; the phenomenon is called helium flash.

Q11. What are the main processes of neucleosynthesis in the star?Ans. Proton-proton chain reaction and the carbon-nitrogen-oxygen

cycle are the two main processes of neucleosynthesis in the star.

Q12. What are the techniques employed to determine the magnitudes of the Variable stars?

Ans. The three techniques most commonly employed are as following:

a. The magnitude of the variable is estimated by visual observation through the telescope, by comparing its brightness of neighboring star of known magnitude.

b. The magnitude of the variable star is measured by comparing its image with the image of comparing star on a telescope.

c. The magnitude of the variable is determined by photoelectric photometry

Q13. What are the types of variable stars?Ans. Different types of the variable stars are:

Pulsating Variables

Eruptive Variables

Eclipsing Variables

Long period Variables

Cepheid Variables

RR LyraeQ14. What are the Binary stars?Ans. Stars around the sun those are found in pairs (binary stars) or

in a system of three or more, ranging upto cluster of thousands each star moving under the combined gravitational influence of other are called binary stars.

Q15. What are the types of the Binary star?

Ans. The types of Binary stars are:

Optical Doubles

Visual Binaries

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Astrometric Binaries

Spectroscopic Binaries

Spectrum Binaries

Eclipsing Binaries

Study QuestionsQ1. What is the main features of H-R diagram?Q2. Write a note on mechanisms of the formation of Protostar? Q3. Explain the evolution of the Young Star?Q4. How the stars evolve from the main sequence to giants?Q5. Discuss the evolution of stars to Red Giants?Q6. What is zero-age main sequence?Q7. What are the sequences of events that occur in the final stage

of evolution of a Star?Q8. Write a note on:

Chemical composition or Metallicity of a star Stellar Nucleosynthesis

Q9. What are Variable Stars? How they are designated? Discuss the typical light curve of a variable star?

Q10. Explain different types of variable Stars.Q11. What are Binary Stars? How they are discovered?Q12. What are the different types of binary star systems? Explain?

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Chapter 7

Subrahmanyan Chandrasekhar,  FRS  (October 19, 1910 – August 21, 1995) was an Indian American astrophysicist. He was a Nobel laureate in physics along with William Alfred Fowler for their work in the theoretical structure and evolution of stars  He was the nephew of Indian

Nobel Laureate Sir C. V. Raman.

White Dwarf one Final Stage of Stellar Evolution

Sooner or later a star must exhaust its store of nuclear energy. Thus it can only contract and release gravitational potential energy. Eventually, the shrinking star will attain enormous density ranging upto over one million times that of water.

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7.1 White dwarfThe first white dwarf was discovered as the companion to Sirius, the brightest appearing star in the sky from its wavy proper motion. Sirius was known to have a companion since 1844. It was first seen telescopically in 1862. Sirius is the brightest star in the constellation Canis Major, Orion’s big dog. It is interesting that Procyon, the brightest star in Orion’s other dog, Canis Minor, Also has a white dwarf companion. A third nearby star with a white dwarf companion is 40 Eridani. The companion of Sirius has a mass of about 94 percent that of the sun. From its temperature and luminosity we find its diameter to be only two percent of that of the sun or about twice that of the earth. The white dwarf has a mean density more than hundred thousand times that of the sun and sixth of the million times that of water. Some white dwarfs have much higher mean densities, and many have central densities in excess of 107 times that of water. A teaspoon full of such material would weigh nearly 50 tons.

7.2 Structure of White Dwarf

The structure of the white dwarfs was first studied by R. H. Fowler, White dwarfs are simpler than most of the stars because the pressure that supports a white dwarf in hydrostatic equilibrium is supplied almost by degenerate electrons and therefore, does not depend on temperature, but only on the density. We know that the volume to which a star can be compressed before the electron become degenerate depends on amount of the gravitational potential energy that can be released by the collapsing star, which in turn depends on the mass. The size of white dwarf, therefore, depends on its mass- the more massive the white dwarf, the smaller its size. A white dwarf of one solar mass must have a radius of about one percent of the sun- about the size of the earth. In more massive white dwarfs some of the electrons have the speed that are an appreciable fraction of that of light, a rigorous treatment must include the effect of special theory of relativity.

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Figure 7.1. A white dwarf star in orbit around Sirius (artist's impression). NASA image

The first such rigorous model of white dwarfs was constructed by Indian astrophysicist S. Chandrasekhar. The analysis by Chandrasekhar shows that white dwarfs of masses successively greater than the sun’s are successively smaller than one percent of its radius, until a mass of 1.4 solar masses is reached, at which point the electrons do not become degenerate and hydrostatic equilibrium cannot be achieved Figure 7.2, thus 1.4 solar mass is the upper limit to the mass of white dwarf. A more massive star must continue to collapse to a far smaller size.

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Figure 7.2 Theoretical relation between the masses and radii of white dwarf stars.

Now those stars that have had time to exhaust their nuclear fuel supply and evolve to a white dwarf stage must have had original masses greater than 1.4 solar masses, for those more massive stars are the very ones that use up their energy store most rapidly. But in such stars electrons do not become degenerate, and star cannot become white dwarf. On the other hand, white dwarf stars are plentiful and they must have come from somewhere. To account for most or all evolved stars of original mass greater than 1.4 solar masses. It is thought therefore, that most stars eventually become white dwarfs. Consequently, they must lower their masses some how, before reaching the stage, by ejecting matter into space.

White dwarfs have hot interior-tens of millions of Kelvin. At this temperature and at the high densities of these stars any remaining hydrogen would undergo violent fusion into helium, giving the luminosity many times higher than observed. Consequently, white dwarfs can have no hydrogen. Their most probable internal composition is a mixture of carbon and oxygen, the principal product of hydrogen burning

Recent studies indicate that at least some white dwarfs probably have cores in which the matter has crystallized. Some also have very strong magnetic fields- upto hundred of millions of Gauss. Moreover, a few display light varieties with period of several minutes. Further, an evolved, average-size star after shedding its outer layers as a planetary nebula shrinks to a relatively tiny object (about the size of Earth) that is not massive enough for further compression to take place, known as a white dwarf. The electron-degenerate matter inside a white dwarf is no longer plasma, even though stars are generally referred to as being spheres of plasma. White dwarfs will eventually fade into black dwarfs over a very long stretch of time.

7.3 Eruptive Stars

There are many types of eruptive variable stars; they range from the flare (or UV Ceti) stars, which display occasional sudden flare-ups in brightness, through the novae, to a spectacular supernova

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I. Novae

These are most famous eruptive variables. Novae, means “new”. Actually novae are an existing star that suddenly emits an outburst of light. In ancient times, when such an outburst brought a star’s luminosity upto naked eye visibility, it seems like a new star. Novae remain bright for only few days or weeks and then gradually fade. They seldom remain visible to the unaided eyes for more than few months. The Chinese, whose annals record novae from centuries before Christ, called them “guest stars”. Only occasionally novae visible to naked eye, but, on average two or three are found telescopically every year. Many may escape detection altogether, they may be as many as two or three dozen nova outburst per year in our Galaxy. The light curve of typical nova is as shown in Figure7.3. According to currently favored theory, novae occur in close binary star system. In each of which one member is a star transferring mass to white dwarfs. All novae recur on some time scale or other; the most violent classic novae, which reached the visible magnitudes of -6 to -9, may wait hundred or thousands of years or more between outbursts.

II. Supernovae

Among the more spectacular of the cataclysm of nature is the supernova. In contrast to an ordinary nova, this increases in luminosity a paltry few thousands or at most tens of thousands of times. As fusion continues in larger stars, until the iron core has grown so large (more than 1.4 solar masses) that it can no longer support its own mass. The core suddenly collapse as its electrons are driven into its protons, forming neutrons and neutrinos in a burst of inverse beta decay, or electron capture. The shockwave formed by this sudden collapse causes the rest of the star to explode in a supernova. Supernovae are so bright that they may briefly outshine the star's entire home galaxy. When they occur within the Milky Way, supernovae have historically been observed by naked-eye observers as "new stars" where none existed before. At maximum light, supernova reaches absolute magnitude -14 to -18 or probably even -20. The three most famous supernovae have been observed during last ten centuries in our Galaxy they are (1) The Supernova of 1054

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in Taurus (described in Chinese annals) (2) Tycho’s “star” of 1572 in constellation Cassiopeia, and (3) the supernova of 1604 in Serpens, described by both Kepler and Galileo. In a typical galaxy supernovae occur at the rate of one every 100 years. The light curve of supernova is similar to that of an ordinary nova expect for the far greater luminosity of supernova and its duration.

Figure 7.3 Light curve of Nova Puppis 1942.

There are several kinds of supernovae, but they all rise to maximum light extremely quickly (in few days or less) and for a brief time. Just after the maximum, the gradual decline sets in, and the star fades until it disappears from telescopic visibility within a few months or years after its outburst. Bright emission lines are observed in the spectra of supernovae indicating that they eject material at the time of outburst like ordinary novae. The velocity of ejection can be upto 10, 000 Km/s. Further, large amount of material is ejected; in fact, the large fraction of original star may go off in the expanding envelope. The blown-off outer layers of dying stars include heavy elements which may be recycled during new star formation. These heavy elements allow the formation of rocky planets. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium. Most of the matter in the star is blown away by the supernovae explosion (forming nebulae such as the Crab Nebula and what remains will be a neutron star (which sometimes manifests itself as a pulsar or X-ray burster) or, in the case of the largest stars (large enough to leave a stellar remnant greater than roughly 4 solar masses), a black hole. In a neutron star the matter is in a state known as neutron-degenerate matter, with a

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more exotic form of degenerate matter, QCD matter, possibly present in the core. Within a black hole the matter is in a state that is not currently understood.

Figure 7.4 The Crab Nebula, remnants of a supernova that was first observed around 1050 AD

7.4 Chandrasekhar limit

Chandrasekhar limit limits the mass of bodies made from electron-degenerate matter-a dense form of matter which consists of nuclei immersed in a gas of electrons. The limit is the maximum nonrotating mass which can be supported against gravitational collapse by electron degeneracy pressure. It is named after the Indian astrophysicist Subramanian Chandrasekhar, and is commonly given as being about 1.4 solar masses. As white dwarfs are composed of electron-degenerate matter, no nonrotating white dwarf can be heavier than the Chandrasekhar limit.

Stars produce energy through nuclear fusion, producing heavier elements from lighter ones. The heat generated from these reactions prevents gravitational collapse of the star. Over time, the star builds up a central core which consists of elements which the temperature at the center of the star is not sufficient to fuse. For main-sequence

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stars with a mass below approximately 8 solar masses, the mass of this core will remain below the Chandrasekhar limit, and they will eventually lose mass (as planetary nebulae) until only the core, which becomes a white dwarf, remains. Stars with higher mass will develop a degenerate core whose mass will grow until it exceeds the limit. At this point the star will explode in a core-collapse supernova, leaving behind either a neutron star or a black hole.

Computed values for the limit will vary depending on the approximations used, the nuclear composition of the mass, and the temperature. Chandrasekhar. Gives a value of

Here, μe is the average molecular weight per electron, mH is the mass of the hydrogen atom, and ω3

0≈2.018236 is a constant connected with the solution to the Lane-Emden equation. Numerically, this value is approximately (2/μe)2 · 2.85 · 1030 kg, or 1.43 (2/μe)2 M☉, where

M☉=1.989·1030 kg is the standard solar mass, As is the Planck mass, MPl≈2.176·10−8 kg, the limit is of the order of MPl

3/mH2.

Electron degeneracy pressure is a quantum-mechanical effect arising from the Pauli Exclusion Principle. Since electrons are fermions, no two electrons can be in the same state, so not all electrons can be in the minimum-energy level. Rather, electrons must occupy a band of energy levels. Compression of the electron gas increases the number of electrons in a given volume and raises the maximum energy level in the occupied band. Therefore, the energy of the electrons will increase upon compression, so pressure must be exerted on the electron gas to compress it. This is the origin of electron degeneracy pressure.

In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form P=K1ρ5/3. Solving the hydrostatic equation leads to a model white dwarf which is a polytrope of index 3/2 and therefore has radius inversely proportional to the cube root of its mass, and volume inversely proportional to its mass. As the mass of a model white dwarf increases, the typical energies to which

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degeneracy pressure forces the electrons are no longer negligible relative to their rest masses.

Figure 7.5 Radius-mass relations for a model white dwarf. The lower curve uses the general pressure law for an ideal Fermi gas, while the upper curve is for a non-relativistic ideal Fermi gas. The vertical line marks the ultra-relativistic limit.

The velocities of the electrons approach the speed of light, and special relativity must be taken into account. In the strongly relativistic limit, we find that the equation of state takes the form P=K2ρ4/3. This will yield a polytrope of index 3, which will have a total mass, M limit

say, depending only on K2.

For a fully relativistic treatment, the equation of state used will interpolate between the equations P=K1ρ5/3 for small ρ and P=K2ρ4/3

for large ρ. When this is done, the model radius still decreases with mass, but becomes zero at Mlimit. This is the Chandrasekhar limit. The curves of radius against mass for the non-relativistic and relativistic models are shown in the graph. They are colored blue and green, respectively. μe has been set equal to 2. Radius is measured in standard solar radii or kilometers, and mass in standard solar masses.

A more accurate value of the limit than that given by this simple model requires adjusting for various factors, including electrostatic interactions between the electrons and nuclei and effects caused by nonzero temperature. Lieb and Yau have given a rigorous derivation of the limit from a relativistic many-particle Schrödinger equation.

1. Applications

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The core of a star is kept from collapsing by the heat generated by the fusion of nuclei of lighter elements into heavier ones. At various points in a star's life, the nuclei required for this process will be exhausted, and the core will collapse, causing it to become denser and hotter. A critical situation arises when iron accumulates in the core, since iron nuclei are incapable of generating further energy through fusion. If the core becomes sufficiently dense, electron degeneracy pressure will play a significant part in stabilizing it against gravitational collapse. If a main-sequence star is not too massive (less than approximately 8 solar masses), it will eventually shed enough mass to form a white dwarf having mass below the Chandrasekhar limit, which will consist of the former core of the star. For more massive stars, electron degeneracy pressure will not keep the iron core from collapsing to very great density, leading to formation of a neutron star, black hole, or, speculatively, a quark star. (For very massive, low-metallicity stars, it is also possible that instabilities will destroy the star completely.) During the collapse, neutrons are formed by the capture of electrons by protons in the process of inverse beta decay, leading to the emission of neutrinos. .

The decrease in gravitational potential energy of the collapsing core releases a large amount of energy which is on the order of 1046 joules (100 foes.) Most of this energy is carried away by the emitted neutrinos. This process is believed to be responsible for supernovae of types Ib, Ic, and II. Type Ia supernovae derive their energy from runaway fusion of the nuclei in the interior of a white dwarf. This fate may befall carbon-oxygen white dwarfs that accrete matter from a companion giant star, leading to a steadily increasing mass. It is believed that, as the white dwarf's mass approaches the Chandrasekhar limit, its central density increases, and, as a result of compressional heating, its temperature also increases. This results in an increasing rate of fusion reactions, eventually igniting a thermonuclear flame which causes the supernova. Strong indications of the reliability of Chandrasekhar's formula are:

1. Only one white dwarf with a mass greater than Chandrasekhar's limit has ever been observed. (See below.)

2. The absolute magnitudes of supernovae of Type Ia are all approximately the same; at maximum luminosity, MV is approximately -19.3, with a standard deviation of no more than 0.3. A 1-sigma interval therefore represents a factor of less than

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2 in luminosity. This seems to indicate that all type Ia supernovae convert approximately the same amount of mass to energy.

7.5 A type Ia supernova apparently from a supra-limit white dwarf

On April 2003, the Supernova Legacy Survey observed a type Ia supernova, designated SNLS-03D3bb, in a galaxy approximately 4 billion light years away. According to a group of astronomers at the University of Toronto and elsewhere, the observations of this supernova are best explained by assuming that it arose from a white dwarf which grew to twice the mass of the Sun before exploding. They believe that the star, dubbed the "Champagne Supernova" by University of Oklahoma astronomer David R. Branch, may have been spinning so fast that centrifugal force allowed it to exceed the limit. Alternatively, the supernova may have resulted from the merger of two white dwarfs, so that the limit was only violated momentarily. Nevertheless, they point out that this observation poses a challenge to us.

7.6 Neutron Star

The discovery of Neutron by Chadwick in 1932 led to the speculation by theoreticians that if the matter in the star could be subjected to such high pressure as to force the free electrons into atomic nucleus, the star could become a body composed entirely of neutrons. Walter Baade and Fritz Zwicky suggested that supernova expositions might form neutron stars. At least some pulsers are associated with the remnants of supernovae. Then it was wondered if pulsers are the neutron stars.

Neutrons like electrons, obey Pauli’s principle and can become degenerate if crowded into a sufficiently small volume for a given momentum range, so perhaps a star could collapse into degenerate neutrons if it somehow escaped becoming the white dwarf. The neutron in such condition could not decay into proton and electron, for, by the time the star is that collapsed, the allowable states for electrons would be filled. The structure of the neutron star is analogous to white dwarf except that neutron stars are much smaller.

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A Neutron star of one solar mass would have the density of 1014 to 1015 g/cm3 –comparable to that of atomic nucleus itself, and it will have the radius of 10 Km. As indicated in the Table 7.1 a star of such dimensions would have the natural period of pulsation of less than one ten-thousandth of a second. Since a neutron star could rotate with any period much longer than this, it is believed that pulsars are the rotating neutron stars.

Radius (Solar Radii) Period Examples1000 4 yr Red Supergiants100 1 month Cephides10 1 day RR Lyra stars1 1 hr Sun

0.1 2 min0.01 4 s White dwarf10-5 10-4 s Neutron star

Table 7.1 Pulsation periods of various stars of One Solar Mass.

Their exist mass-radius relationship for neutron star, an upper mass limit as well, although the exact theory ids not yet certain, the mass limit for a neutron star is believed to be from 2 to 3 solar masses. The upper mass limit for a neutron star exceeds that for white dwarfs, a star of mass greater than 1.4 solar masses could gravitationally contract to a neutron star, missing the white dwarf configuration. Further, it is also believed that neutron stars are formed in supernova explosions. It seems unlikely that a star of less than 1.4 solar masses can become supernova unless it is first a white dwarf that is a member of a close binary star system. Suppose its mass is very close to the upper limit for the masses of white dwarfs and that the companion star is a giant that is transferring some of its matter to the dwarf. As the transferring material pours into white dwarf, it can raise its mass above the limiting value for stable white dwarf; then there is nothing to stop it from collapsing into a neutron star.

7.7 Black Hole

In 1796 the French mathematician Pierre Simon Laplace speculated about the properties of an object that had so great a gravitational field that a light cannot escape at all. It would bend the light around to stay

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with the object. Laplace’s “Corps Obscurs” were later reconsidered by modern physicists, armed with the new rigor of general relativity theory. John Wheeler, the Princeton physicist who had become intimately associated with general relativity, has dubbed such objects “black holes”. Consider the light radiated from the surface of a neutron star. That which emerges normal to the surface flows out radially from the star. That emitted at an angle of say 30˚ to the normal leaves the star at an angle some what greater than 30˚to the normal, because of gravitational deflection. Now imagine a more massive star that shrinks to a smaller size and high density than neutron star. As the surface gravity increases, the deflection of light increases too. Eventually, a star reaches a size at which a horizontal beam of light enters a circular orbit. A surface of that radius is called is called Photon sphere. As the star shrinks to a size smaller than the photon sphere, to escape the starlight must flow into a cone about the normal to the surface of half angle θ as indicated in Figure 7.6 and light at greater angle fall back on star. The angle become smaller and smaller as the star collapses until the radius of the star is two third of photon sphere near the star θ becomes zero, and no light at all can escape. At this point the velocity of escape from the star equals to the velocity of light. As the star contracts further more light and everything else is trapped inside, unable to escape through the surface where the escape velocity is velocity of light. The surface is called event horizon and its radius is called Schwarzschild radius, named for Karl Schwarzschild, who first described the situation a few years after Einstein introduced general relativity. This surface is the boundary of the black hole. All that is inside is hidden forever from us; as the star shrinks through the event horizon it disappears from the universe.

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Figure 7.6 The deflection of light from a very dense star. At the radius smaller than the photon sphere to escape light must flow into a cone of half angle θ with respect to the normal n, to the surface. At the event horizon θ = 0. (35.10)

The size of Schwarzschild radius is proportional to the mass of the star. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass through

Where is the Schwarzschild radius and is the mass of the Sun.

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For a star of one solar mass, the black hole is about 3 Km in diameter, thus the entire black hole, some 6 Km in diameter is about one third the size of the neutron star. The event horizon of larger and smaller black holes-if they exist-has greater and lesser radii respectively. For example, if earth to become black hole it would have to be compressed to the radius of only 1 cm or about the size of a golf ball. But should black hole exist? For stars of less than about 1.4 solar masses can become white dwarfs. Those with larger mass, we think can exist as neutron star, but there is an upper limit to the mass of neutron stars; we thin the limit is not over three solar masses. We know the tiny fraction of all stars have still greater mass. What becomes of them when they exhaust their store of nuclear fuel? Perhaps they eject part of their mass (as planetary nebula or supernova outburst) so that what is left can contract to a white dwarf or neutron star. But what if they do not? Then we know no other fate for such massive stars then that they become black holes. Thus we are not certain that any star must ever have to become a black hole, but we have good reasons to expect that many massive stars albeit a minority of all stars can end up in that exotic state. How then do we find a black hole, which of course we cannot see? We can detect it by its gravitational effects on other stars (as star collapse into black holes they leave behind their gravitational fields), and this is most easily accomplished in a binary star system.

1. Possible Candidates

In order to find a black hole we must (a) find a star whose motion showed it to be a member of a binary star system, and so have a companion of mass too high to be a white dwarf or neutron star (b) that, the companion star must not be visible, for a black hole gives no light. But being invisible not enough, for relatively faint star must be unseen next to the light of a brilliant companion therefore, (c) we must have evidence that the unseen star, of mass too high to be a neutron star is also a collapsed object of extremely small size for then our theory predicts that it must be a black hole or least a star on the way to becoming one, Modern space astronomy supports (c) One way to know we have a small object of high gravity (and possibly a black hole) is if matter falling toward or into it is accelerated to high speed. Near the event horizon of a black hole, matter is moving at near the speed of light, internal friction can heat it to very high

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temperatures-up to 100 million Kelvins or more. Such hot matter emits radiation in the form of X-rays. Modern orbiting X-ray telescopes-especially the Einstein telescope, HEAO 2- can and does reveal such intense source of X-radiation. Thus we require X-ray sources associated with binary stars with invisible companions of high mass. We cannot prove that such a system contains a black hole, but at present we have no other theory for what the invisible massive companion can be if the X-rays are coming from gas heated by falling toward it. Consider one star in such a double star system has evolve to a black hole and that the second star has now evolved to a red giant so large that its outer layer pass through a point of no return between the star and some of its matter falls to the black hole. The mutual revolution of the giant star and black hole cause the material from the former to flow not directly to black hole but to conserve angular momentum it spirals around the black hole and is collected in a flat disk of matter called the accretion disk, In the inner part of the accretion disk the matter is revolving about the black hole so fast that its internal friction heat it upto the temperature where it emits X-rays. In the course of this friction, some material in the accretion disk is given extra momentum, and escape from the double star system and the other material loses momentum and fall into black hole. Yet another way to form an accretion disk in a binary star system is from material ejected from a companion of the black hole as a stellar wind some of the ejected gas will flow close enough to the black hole to be captured by it into the disk. Such is the case of binary system containing first X-ray source discovered in Cygnus-Cygnus X-1. The variable star as shown in Figure 7.7 is a normal B type star. The spectroscopic observations show it to have an unseen companion of mass near ten times that of the sun. The companion would be a black hole if it ever a small, collapsed object. The X-rays from it strongly suggest that it is, for we have no other explanation for the source of those x-rays than gas heated by an infall toward a tiny massive object. Of course we cannot be certain Cygnus X-1 is a black hole, but many astronomers think that it probably is.

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Figure 7.7 In visible light CygnusX-1 appears as an Ordinary star.

Figure 7.8 An artist's concept of Cygnus X-1 shows hot gas from the giant blue star flowing toward the black hole, forming a bright accretion disk.

2. Properties

There seems to be much folklore about black holes, many of them are misleading. One idea is that black holes are the monsters that go about sucking things up with their gravity. Actually, the gravitational attraction surrounding the black hole at a large distance is the same as that around other star (or object) of same mass. Even if another star or space ship was to pass one or two solar radii from the black hole. Newton’s law gives an excellent account of what would happen to it. But very near to the surface of the black hole the gravitation is

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so strong that Newton’s law break down, For a black hole of mass of the sun light would have to come within 4.5 Km of its center to be trapped. A solar mass black hole, is only 3 Km in radius which is very tiny target. Even collisions between ordinary stars, hundreds of thousands times bigger in diameter are so rare as to be essentially nonexistent. A star would be far, far safer to us as an interloping black hole than it would have been in its former stellar dimensions.

Ideas about Black Holes

The black holes need not be limited to stellar masses. There has been considerable consideration of the possibilities of vary large amount of gas collecting together and collapsing into black hole in center of globular clusters, galaxies, or even clusters of galaxies. A mass of gas collapsing into a black hole releases more than 100 times as much energy as can be extracted from the same mass through the nuclear fusion. Thus the gravitational collapse of a million solar masses of gas into a black hole at the center of the galaxy could produce prodigious amount of released gravitational potential energy. However, there is a great deal of speculation about such processes which account for the energy of quasars and other phenomenal objects. It may well be that through massive black holes general relativity theory will be found to have profound consequences in modern astrophysics.British theoretical astrophysics Stephen Hawking suggested that the black holes microscopic levels (or less than few solar masses) could have been produced in the big bang at the origin of universe. If it is so, then they would involve quantum mechanics as well as relativity in the most amazing way. We know that all fundamental particles have antiparticles for example electrons and positrons, protons and antiprotons, and so on. Whenever the particle and its antiparticle come into contact, they annihilate each other transforming completely into energy. Similarly, pure energy can be converted into pairs of particles – an electron and positron, through a pair production and observed regularly in the nuclear physics laboratory. All this is possible because mass and energy are equivalent, but obviously mass cannot be created from nothing - we need energy to do it. Yet, according to quantum theory, it is possible for matter (or energy) to be created from nothing for an exceedingly brief period of time. This is possible because of innate uncertainty in nature, at the microscopic

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level, of the measures of the physical quantities such as mass and energy. This does not violates the conservation laws, because any matter that come into being almost immediately disappears again spontaneously, so on average mass and energy (combined) is conserved. As per Hawking if a positron and electron come into existence momentarily in the vicinity of a black hole. There is a chance that one or the other will fall into hole and hence not be able to annihilate with its antiparticle, returning the energy it borrowed from the nature. Its antiparticle cannot escape unscathed. Many such positrons and electrons so created near the black holes and escaping from them do annihilate each other, creating energy. Now that energy cannot come from nothing. According to Hawking’s theory it must come from black hole itself. Robbing the black hole of energy in this way robs off its mass (E=mc2) so black hole must slowly evaporate through this process of pair production. This process is only important, near very tiny black holes. Solar-mass black hole would evaporate in this way at absolute negligible rate. In fact, the only black holes that would have had time to so evaporate in the age of universe would be those of original mass less than about 1025g like minor planet. Smaller ones would already be gone because evaporation rate increases with the decrease of mass of black holes, at the end one would go off explosively emitting a final burst of gamma radiation. It is not yet clear about the formation of such mini black holes and their evaporation process.

7.8 Star Clusters

The study of star clusters is very important, because the stars in the single cluster are at about the same distance from the earth; consequently, their luminosities, colours and so on can be compared easily and accurately. Moreover, the stars in the cluster have common origin, being formed about same time from same prestellar material. A number of star clusters bears popular names of mythological characters (the Pleiades) the other clusters bears the names of constellations in which they appear (the double cluster of Perseus)

1. Descriptions

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A cluster that contains a great many stars are said to be rich clusters, poor clusters, on the other hand contains comparatively few stars. Rich clusters are likely to be conspicuous, and their identification as genuine stellar systems is certain. Poor clusters, on the other hand, are much more difficult to pick out against background of the general star field. Most of the clusters that are cataloged contains a high enough density of stars to stand out against the background so that there is virtually no chance of their being accidental superposition of stars at different distances. Even so, it is often difficult or impossible to say which certainty whether a given individual star is a member of a cluster or not. In general a few of the stars studied as a cluster members are actually stars in background or foreground.

2. Globular Clusters

About hundred globular clusters are known some of them in a halo and nucleus of our Galaxy. They all are very far from the sun; some are found at the distance of 60,000 L.Y. or more from galactic plane. Few of them bright enough to be seen with the naked eye, they appear to be faint, fuzzy stars. One of the most famous naked eye globule clusters is M13 in the constellation Hercules. A small telescope reveals the brightest star while a large telescope shows them to be beautiful, globe shaped system of stars. A good photograph of typical globular cluster shows it to be nearly circular symmetrical systems of stars with the highest concentration of stars near its own center. Most of the stars in the central regions of the clusters are not resolved as individual points of light but appears as nebulous glow. Photograph of globular clusters shows that the brightest stars are red. These stars are two or three magnitude brighter than the RR-Lyrae variable stars that are almost always found in the globular clusters Since RR-Lyrae stars average about absolute magnitude 0 to +1, the brightest star must be red giants. The other kinds of variables sometimes found in globular clusters include type II Cepheids and RV Tauri stars. One cluster (NGC 7078) contains a planetary nebula. Distances to the globular clusters are calculated from the apparent magnitudes of RR Lyrae stars they contain. From angular sizes their actual linear diameter are found to be from 20 to 100 PC or more. In one of the nearest globular cluster more than 30,000 stars have been counted. Most of the clusters

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contain hundreds of thousands of member stars. The combined light from all these stars gives a globular cluster an absolute magnitude in the range -5 to -10. The average density of globular cluster is about 0.4 stars per cubic parsec. In a dense center of globular cluster the star density may be as high as 100 or 1000 per cubic parsec. The motion of globular clusters reveals that they are high velocity objects that do not partake of general galactic rotation. They are believed to revolve about the nucleus of the galaxy on the orbits of high eccentricity and high inclination to the galactic plane. A typical cluster probably has the period of revolution of the order of 108 years.

3. Open Clusters

They appear comparatively loose and open. They contain far fewer stars than globular clusters and show little or no strong concentration of stars towards their own centers. Although open clusters are usually more or less round in appearance they lack high degree of spherical symmetry. Some open clusters are usually fully resolved, even in its center. They are found in the disk of the galaxy often associated with interstellar matter. Due to their locations they are sometimes called galactic clusters. They are low velocity objects and belong to stellar population I they are presumed to be originated near the spiral arms. Over 1000 open clusters have been identified till 1982. Several open clusters are visible to unaided eye. Most famous among them is Pleiades that appears as a group of six stars as shown in Figure 7.8 Typical open cluster contain several dozen to several hundred member stars, although few such as M67 contain more than thousand stars. Open clusters usually have the diameter of less than 10 pc. Bright supergiants stars of high luminosity in some open clusters may cause them to outshine globular clusters. The RR Lyrae stars are never found in open clusters but other kinds of variable stars, such as type I Cepheids, are some times present.

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Figure 7.9 The Pleiades, an open cluster of stars in the constellation of Taurus.

4. Associations

It is known for more than 50 years that most luminous main – sequence stars of spectral types O and B are not distributed at random in the sky but tends to be grouped into associations, lying along spiral arms of our Galaxy. Soviet astronomer V. A. Ambartsumian pointed out that they must be very young group of stars. Because the stars of association lie in the galactic plane and are spread over tens of parsecs, each revolves about the galactic center with a slightly different orbital speed. There are two kinds of associations those containing O and B stars called O-associations and the other containing T Tauri stars are called T- associations. About 70 percent associations have been catalogued. The characteristics of star clusters are shown in Table-7.2.

Globular Clusters

Open Clusters Associations

Number Known in Galaxy

125 1055 70

Location in Galaxy Halo and Nuclear bulge

Disk (and spiral arms)

Spiral Arm

Diameter (pc) 20 to 100 <10 30 to 200Mass (solar masses) 104 to 105 102 to 103 102 to 103?Number of stars 104 to 105 50 to 103 10 to 100?Colour of the brightest star

Red Red or Blue Blue

Integrated absolute -5 to -10 0 to - 10 -6 to - 11

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visual magnitude of clusterDensity of stars (solar masses per parsec)

0.5 to 1000 0.1 to 10 <0.01

Examples Hercules Cluster (M13)

Hyades, Pleiades Zeta Persei, Orion

Table-7.2.Characteristics of Star Clusters.

Continuous as the stars that shineAnd twinkle on the milky way,

They stretch'd in never-ending lineAlong the margin of a bay:

Ten thousand saw I at a glanceTossing their heads in sprightly dance.

— William Wordsworth, 'I Wandered Lonely as a Cloud' (also known as 'The Daffodils'), 1804.

Summery

1. The first white dwarf was discovered as the companion to Sirius.

2. The volume to which a star can be compressed before the electron become degenerate depends on amount of the gravitational potential energy that can be released by the collapsing star, which in turn depends on the mass.

3. Size of white dwarf, therefore, depends on its mass- the more massive the white dwarf, the smaller its size.

4. Novae are an existing star that suddenly emits an outburst of light.

5. Supernova are the more spectacular of the cataclysm of nature is the.

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6. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.

7. Chandrasekhar limit limits the mass of bodies made from electron-degenerate matter-a dense form of matter which consists of nuclei immersed in a gas of electrons.

8. Only one white dwarf with a mass greater than Chandrasekhar's limit has ever been observed.

9. Structure of the neutron star is analogous to white dwarf except that neutron stars are much smaller.

10. The mass limit for a neutron star is believed to be from 2 to 3 solar masses.

11. The size of Schwarzschild radius is proportional to the mass of the star.

12. If earth to become black hole it would have to be compressed to the radius of only 1 cm or about the size of a golf ball.

13. For a black hole of mass of the sun light would have to come within 4.5 Km of its center to be trapped.

14. A solar mass black hole, is only 3 Km in radius which is very tiny target

15. The stars in the cluster have common origin, being formed about same time from same prestellar material.

Exercises Fill in the blanks

1 The first white dwarf was discovered as the companion to _______.

2 The white dwarf has a mean density more than hundred thousand times that of __________ and sixth of the million times that of ____________.

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3 The size of white dwarf, therefore, depends on its __________.4 _________Solar mass is the upper limit to the mass of white

dwarf.5 White dwarfs can have no ______________.6 Recent studies indicate that at least some white dwarfs

probably have cores in which the matter has _____________.7 Novae remain bright for only __________ or weeks and then

gradually fade.8 Supernovae are so bright that they may briefly outshine the

star's entire home ______________.9 No nonrotating white dwarf can be ___________ than the

Chandrasekhar limit.10 The structure of the neutron star is analogous to white dwarf

except that neutron stars are much _____________.11 ___________ are the object that had so great a gravitational

field that a light cannot escape at all

Short questions with answer

Q1. When a star can release gravitational potential energy?Ans. star must exhaust its store of nuclear energy only then it can

contract and release gravitational potential energy.Q2. What is the mean density of the white dwarf?Ans. The white dwarf has a mean density more than hundred

thousand times that of the sun and sixth of the million times that of water. Some white dwarfs have much higher mean densities, and many have central densities in excess of 107 times that of water. A teaspoon full of such material would weigh nearly 50 tons.

Q3. Compression of a star is dependent on? Ans. Volume to which a star can be compressed before the electron

become degenerate depends on amount of the gravitational potential energy that can be released by the collapsing star, which in turn depends on the mass.

Q4. What do we learn from analysis by Chandrasekhar?Ans. The analysis by Chandrasekhar shows that white dwarfs of

masses successively greater than the sun’s are successively smaller than one percent of its radius, until a mass of 1.4 solar masses is reached, at which point the electrons do not become degenerate and hydrostatic equilibrium cannot be achieved.

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Q5. What is the internal composition of white dwarf?Ans. The most probable internal composition of white dwarf is a

mixture of carbon and oxygen, the principal product of hydrogen burning. Recent studies indicate that at least some white dwarfs probably have cores in which the matter has crystallized.

Q6. What is the difference between a star and white dwarf?Ans. The electron-degenerate matter inside a white dwarf is no

longer plasma, even though stars are generally referred to as being spheres of plasma.

Q7. What Novae? What is their period of their optical visibility?Ans. Novae are an existing star that suddenly emits an outburst of

light. Novae remain bright for only few days or weeks and then gradually fade. They seldom remain visible to the unaided eyes for more than few months.

Q8. When a star can release gravitational potential energy?Ans. Supernova is most spectacular cataclysm of the nature. In

contrast to an ordinary nova, it increases in luminosity and paltry few thousands or at most tens of thousands of times.

Q9. What is the maximum absolute magnitude reached by Supernova? Name some of the most famous Supernova?

Ans. At maximum light, supernova reaches absolute magnitude -14 to -18 or probably even -20. The three most famous supernovae have been observed during last ten centuries in our Galaxy they are (1) The Supernova of 1054 in Taurus (described in Chinese annals) (2) Tycho’s “star” of 1572 in constellation Cassiopeia, and (3) the supernova of 1604 in Serpens, described by both Kepler and Galileo

Q10. What is the rate of occurrence of the Supernova? What happens to the outflow of the energy from the Supernova?

Ans. In typical galaxy supernovae occur at the rate of one every 100 years. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.

Q11. What is the state of matter in the neutron star?Ans. In a neutron star the matter is in a state known as neutron-

degenerate matter, with a more exotic form of degenerate matter

Q12. What is the structure of the neutron star?

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Ans. The structure of the neutron star is analogous to white dwarf except that neutron stars are much smaller. A Neutron star of one solar mass would have the density of 1014 to 1015 g/cm3 –comparable to that of atomic nucleus itself, and it will have the radius of 10 Km.

Q13. Why the study of star clusters important?Ans. The study of star clusters is very important, because the stars in

the single cluster are at about the same distance from the earth; consequently, their luminosities, colors and so on can be compared easily and accurately.

Q14. How we can differentiate star clusters? What are its different types?

Ans. Cluster that contains a great many stars are said to be rich clusters, poor clusters, on the other hand contains comparatively few stars. They are further classified into:The Globular Clusters those are about hundred in number in a halo and nucleus of our Galaxy, and the Open Clusters which appear comparatively loose and open. They contain far fewer stars than globular clusters and show little or no strong concentration of stars towards their own centers.

Q15What are the types of associations?Ans. There are two kinds of associations those containing O and B

stars called O-associations and the other containing T Tauri stars are called T- associations.

Study QuestionsQ1. What is the white dwarf? When they were discovered?Q2. What is Structure of White Dwarf?Q3. What are Novae?Q4. What are Supernovae? Discuss its light curve? Q5. What is Chandrasekhar limit? Give its applications?Q6. How you can establish the reliability of Chandrasekhar's

formula?Q7. What is supra-limit white dwarf?Q8. What is Neutron Star? What is the relation of its mass with

radius?Q9. What is Black Hole? How it is formed?Q10. What are the possible candidates for the black hole? Q11. What are the Properties of black hole?Q12. What is different idea about the black hole?Q13. Write the note on:

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Schwarzschild radius Globular Clusters Open Clusters Associations

Galaxies

Unit IV

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Chapter 8

Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer who profoundly changed our understanding of the universe by demonstrating the existence of galaxies other than our own, the Milky Way. He also

discovered that the degree of "Doppler shift" (specifically "redshift") observed in the light spectra from other galaxies increased in proportion to a particular galaxy's distance from Earth. This relationship became known as Hubble's law, and helped established.

GalaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy derives from the Greek term for our own galaxy, galaxias (γαλαξίας), or kyklos galaktikos, meaning "milky circle" for its appearance in the sky. In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Hera's breast while she is asleep so that the baby will drink her divine milk and will thus become immortal. Hera wakes up while

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breastfeeding and then realize she is nursing an unknown baby: she pushes the baby away and a jet of her milk sprays the night sky, producing the faint band of light known as the Milky Way. In the astronomical literature, the capitalized word 'Galaxy' is used to refer to our galaxy, the Milky Way, to distinguish it from the billions of other galaxies. The term Milky Way first appeared in the English language in a following poem by Chaucer.

"See yonder, lo, the Galaxyë Which men clepeth the Milky Wey,

 For hit is whyt."—Geoffrey Chaucer The House of Fame, c. 1380.[

8.1 Observation history

The realization that we live in a galaxy, and that there were, in fact, many other galaxies, parallels discoveries that were made about the Milky Way and other nebulae in the night sky.

The Greek philosopher Democritus (450–370 B.C.) proposed that the bright band on the night sky known as the Milky Way might consist of distant stars. Aristotle (384–322 B.C.), however, believed the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together" and that the "ignition takes place in the upper part of the atmosphere, in the region of the world which is continuous with the heavenly motions." The philosopher Olympiodorus the Younger (fl. 540) criticized this view, arguing that if the Milky Way were sublunary it should appear different at different times and places on the Earth, and that it should have parallax, which it does not. In his view, the Milky Way was celestial. This idea would be influential later in the Islamic world.

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Figure 8.1 NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 17,000 parsecs in diameter and approximately 20 million parsecs distant.

The Arabian astronomer, Alhazen (965–1037 A.D.), made the first attempt at observing and measuring the Milky Way's parallax, and he thus "determined that because the Milky Way had no parallax, it was very remote from the earth and did not belong to the atmosphere." The Persian astronomer, Abū Rayhān al-Bīrūnī (973–1048), proposed the Milky Way galaxy to be "a collection of countless fragments of the nature of nebulous stars." IbnBajjah ("Avempace", d. 1138) proposed that the Milky Way was made up of many stars which almost touched one another and appeared to be a continuous image due to the effect of refraction from sublunary material. Ibn Qayyim Al-Jawziyya (1292–1350) proposed the Milky Way galaxy to be "a myriad of tiny stars packed together in the sphere of the fixed stars".

Actual proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is composed of a huge number of faint stars. In 1750 Thomas Wright, in his An original theory or new hypothesis of the Universe, speculated (correctly) that the galaxy might be a rotating body of a huge number of stars held together by gravitational forces, akin to the solar system but on a much larger scale. The resulting disk of stars can be seen as a band on the sky from our perspective inside the disk. In a treatise in 1755, Immanuel Kant

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elaborated on Wright's idea about the structure of the Milky Way and introduced the term ”Island Universe” for these distant nebulae.

Figure 8.2 Galactic Center of Milky Way and a meteor

A very significant contribution to our knowledge of the galaxies was provides by the work of William Herschel and his only son, John (1792-1871). William surveyed the northern sky by scanning it visually with the world’s first large reflecting telescope. Elder Herschel himself discovered thousands of nebulae (plural of nebula) that literally means “clouds”. Faint star clusters glowing gas clouds, dust clouds reflecting starlight, and galaxies all appear as joint unresolved luminous patches when viewed visually with the telescopes of only moderate size, Since the true nature of these objects were not known to early observers , all of them were called nebulae. Today we usually reserve the word “nebula” for the true gas or dust clouds, but some astronomers still refer to galaxies as nebulae or extragalactic nebulae and regarded them as galaxies like Milky Way system; he was known to remark once that he had discovered more than 1500 universes

William Herschel constructed his catalog of deep sky objects, he used the name spiral nebula for certain objects such as M31. These would later be recognized as immense conglomerations of stars, when the true distance to these objects began to be appreciated, and they would be termed island universes. However, the word Universe was understood to mean the entirety of existence, so this expression fell into disuse and the objects instead became known as galaxies

The first attempt to describe the shape of the Milky Way and the position of the Sun in it was carried out by William Herschel in 1785 by carefully counting the number of stars in different regions of the sky. He produced a diagram of the shape of the galaxy with the solar system close to the center. Using a refined approach, Kapteyn in 1920 arrived at the picture of a small (diameter about 15 kiloparsecs)

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ellipsoid galaxy with the Sun close to the center. A different method by Harlow Shapley based on the cataloguing of globular clusters led to a radically different picture: a flat disk with diameter approximately 70 kiloparsecs and the Sun far from the center. Both analyses failed to take into account the absorption of light by interstellar dust present in the galactic plane, but after Robert Julius Trumpler quantified this effect in 1930 by studying open clusters, the present picture of our galaxy, the Milky Way, emerged.

Figure 8.3 The shape of the Milky Way as deduced from star counts by William Herschel in 1785; the solar system was assumed to be near the center.

8.2 Distinction from nebulae

In the 10th century, the Persian astronomer, Abd al-Rahman al-Sufi (known in the West as Azophi), made the earliest recorded observation of the Andromeda Galaxy, describing it as a "small cloud". Al-Sufi also identified the Large Magellanic Cloud, which is visible from Yemen, though not from Isfahan; it was not seen by Europeans until Magellan's voyage in the 16th century. These were the first galaxies other than the Milky Way to be observed from Earth. Al-Sufi published his findings in his Book of Fixed Stars in 964.

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Figure 8.4 Sketch of the Whirlpool Galaxy by Lord Rosse in 1845

In 1054, the creation of the Crab Nebula resulting from the SN 1054 supernova was observed by Chinese, Japanese and Arab/Persian astronomers. The Crab Nebula itself was observed centuries later by John Bevis in 1731, followed by Charles Messier in 1758 and then by the Earl of Rosse in the 1840s.

Toward the end of the 18th century, Charles Messier compiled a catalog containing the 109 brightest nebulae (celestial objects with a nebulous appearance), later followed by a larger catalog of 5,000 nebulae assembled by William Herschel. In 1845, Lord Rosse constructed a new telescope and was able to distinguish between elliptical and spiral nebulae. He also managed to make out individual point sources in some of these nebulae, lending credence to Kant's earlier conjecture. In 1917, Heber Curtis had observed a nova S Andromeda within the "Great Andromeda Nebula" (Messier object M31). Searching the photographic record, he found 11 more novae. Curtis noticed that these novae were, on average, 10 magnitudes fainter than those that occurred within our galaxy. As a result he was able to come up with a distance estimate of 150,000 parsecs. He became a proponent of the so-called "island universes" hypothesis, which holds that spiral nebulae are actually independent galaxies.

Typical galaxies range from dwarfs with as few as ten million (107) stars up to giants with one trillion (1012) stars, all orbiting the galaxy's center of mass. Galaxies can also contain many multiple star systems, star clusters, and various interstellar clouds. The Sun is one

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of the stars in the Milky Way galaxy; the Solar System includes the Earth and all the other objects that orbit the Sun.

Figure 8.5 Photograph of the "Great Andromeda Nebula" from 1899, later identified as the Andromeda Galaxy

In 1920 the so-called Great Debate took place between Harlow Shapley and Heber Curtis, concerning the nature of the Milky Way, spiral nebulae, and the dimensions of the Universe. To support his claim that the Great Andromeda Nebula was an external galaxy, Curtis noted the appearance of dark lanes resembling the dust clouds in the Milky Way, as well as the significant Doppler shift.

The matter was conclusively settled in the early 1920s. In 1922, astronomer Ernst Öpik gave a distance determination which supported the theory that the Andromeda Nebula is indeed a distant extra-galactic object. Using the new 100 inch Mt. Wilson telescope, Edwin Hubble was able to resolve the outer parts of some spiral nebulae as collections of individual stars and identified some Cepheid variables, thus allowing him to estimate the distance to the nebulae: they were far too distant to be part of the Milky Way.

8.3 Types of Galaxies

Galaxies differ a great deal among themselves but majority fall into two general classes; ellipticals and spirals; a minority is classed as irregular

1. Elliptical galaxy

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The elliptical galaxies are spherical ellipsoidal system that is thought to consist almost entirely of old stars; they contain no trace of spiral arms. They are far more numerous than spirals. The elliptical galaxies resemble the nucleus and halo components of spiral galaxies. Although dust and conspicuous emission nebulae are not easily observed in elliptical galaxies some of them show evidence of sparse interstellar gas in their spectra. I the large nearby ones, many globular clusters can be identified. These galaxies show various degree of flattening, ranging from system that are approximately spherical to those that approach the flatness of spirals (Figure 8.6). The distribution of light in a typical elliptical galaxy shows that while it has many stars concentrated toward its center, a sparse scattering of stars extends for very great distances and merges imperceptibly into the void of intergalactic space. It is for this reason it is nearly impossible to define total size of an elliptical galaxy. The elliptical galaxies are not disk shaped this very fact show that they are not rotating rapidly. It is hypothesized that they are systems formed from pregalaxian material that had little angular momentum per unit mass- that is, their original material has low net rotation consequently, as such a cloud of primeval material contracted it did not flatten into a disk, and the density of material was high enough that it completely condensed into stars. Elliptical galaxies have a much greater range in size, mass and luminosity than do the spirals. The rare giant elliptical for example M87 (Figure 8.7) are more luminous than any known spirals, the brightest elliptical in some rich clusters have absolute magnitude that are brighter than -23 that is more than 1012 times the luminosity of the sun (for example, NGC 4886, in coma cluster of galaxies). The mass to light ratio for giant ellipticals is between 20 and 100. Recent Studies by D Jenner shows that some of these galaxies have masses of about 1023 times that of the sun. The diameter of these large galaxies are difficult to define, they extend over at least several hundred thousand light years. These galaxies range from giants to dwarfs. An example is Leo II systems (Figure 8.8) in which there are few bright stars in this galaxy and even its central region is transparent. The total numbers of stars are at least several millions. The absolute magnitude of Leo II system is –

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10, its luminosity is about one million times that of the sun. It is so near to us (about 750,000 L.Y.) that its diameter (abut 500 L.Y.) as limited by tidal force exerted on it by our Galaxy. Between Giant and dwarf elliptical galaxies are systems like M 32 and NGC 205. Many elliptical galaxies are believed to form due to the interaction of galaxies, resulting in a collision and merger. They can grow to enormous sizes (compared to spiral galaxies, for example), and giant elliptical galaxies are often found near the core of large galaxy clusters. Starburst galaxies are the result of such a galactic collision that can result in the formation of an elliptical galaxy.

Figure 8.6 Types of elliptical galaxies

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Figure 8.7 NGC 4486 (M87) giant elliptical galaxy in Virgo. Note the many globular clusters in galaxy.

Figure 8.8 Leo Ii, a dwarf elliptical galaxy

2. Spiral Galaxies

A spiral galaxy consists of a nucleus, a disk, a halo and the spiral arm. Our own Galaxy and M31 are typical example of spiral galaxies. The interstellar material is usually observed in the arm of spiral galaxies. Bright emission nebulae are present, and the absorption of light by dust is also apparent especially in these systems turn almost edge on to our line of sight (Figure 8.9). The spiral arm contains the young stars that include luminous supergiants. These bright stars and the emission nebulae make the arm of spirals stand out like the arm of a fourth- of -July pinwheel. The individual inter-arm stars are usually not observable at all, although their collective light may be appreciable as uniform glow. Open star clusters can be seen in the arms nearer spirals and globular clusters are often visible in their halos in M31, for example, more than 200 globular clusters have been identified. Spiral galaxies contain both young and old stars. Some of the famous spirals are as shown M51 and M33 (Figure 8.10 & 8.11) are seen near face on, NGC4565 (Figure 8.9) is nearly edge on. Note the absorbing line of interstellar dust in NGC 5141(M51) - a thin slab in the

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central plane of disk which is silhouetted against the nucleus, M81 (Figure 8.12), like M31 (Figure 8.13) is viewed obliquely.

Figure 8.9 NGC 4565 a spiral galaxy in Coma Berenices seen edge on.

Figure 8.10 The Sc galaxy NGC 5194 (M51) and its irregular companion NGC 5195.

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Figure 8.11 NGC 598 (M33) a spiral galaxy in Triangulum

Figure 8.12 NGC 3031 (M81) spiral galaxy in Ursa Major

Figure 8.13 The Andromeda Galaxy, M31,

A large minority of spiral galaxies display “bars” running through nuclei; the spiral arms of such a system usually begin from end

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of the bar, rather than winding out directly from the nucleus. These are called “barred spirals”. A famous example is NGC 1300 (Figure 8.14). The bar in the barred spirals is in a sense a straight portion of spiral arm and sometimes contains interstellar matter and young stars.

Figure 8.14 NGC 1300, barred spiral galaxy in Eridanus.

Studies of the rotation of some barred spirals show that their inner parts are rotating approximately as solid wheels. In the absence of differential shearing rotation the straight bar even persist rather than winding up; the detailed structures and dynamics of barred spirals are not yet thoroughly understood. In both normal and barred spirals we observe a gradual transition of morphological types. At one extreme the nucleus is large and luminous, the arms are small and tightly coiled and bright emission nebulae and supergiants stars are inconspicuous. At the other extreme are spirals in which nuclei are small- almost lacking – and the arms are loosely wound, or even wide open. In these later galaxies, there is high degree of resolution of arms into the luminous stars, star clusters, and emission nebulae. Our Galaxy and M31 are both intermediate between these two extremes. Photographs of these spiral galaxies illustrating their transition of types are shown in (Figure 8.15 & Figure 8.16). All spirals and barred spirals rotate in same sense that their arm trail. The diameter of spiral galaxies range from about 20,000 to 100,000 L.Y, the disk halos extends to far greater diameters. Their masses are estimated to range from 109 to 1012 times the mass of the sun. Mass to light ratio of the

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inner part of the spiral galaxies is between 1 and 20. The absolute magnitude of most spirals falls in the range -16 to -21.

3. Barred spiral galaxy

Figure 8.15 Types of Spiral galaxies

Figure 8.16 Types of barred spirals

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Figure 8.17 The Sombrero Galaxy, an example of an unbarred spiral galaxy.

Spiral galaxies consist of a rotating disk of stars and interstellar medium, along with a central bulge of generally older stars. Extending outward from the bulge are relatively bright arms. In the Hubble classification scheme, spiral galaxies are listed as type S, followed by a letter (a, b, or c) that indicates the degree of tightness of the spiral arms and the size of the central bulge. An Sa galaxy has tightly wound, poorly defined arms and possesses a relatively large core region. At the other extreme, a Sc galaxy has open, well-defined arms and a small core region.

In spiral galaxies, the spiral arms do have the shape of approximate logarithmic spirals, a pattern that can be theoretically shown to result from a disturbance in a uniformly rotating mass of stars. Like the stars, the spiral arms also rotate around the center, but they do so with constant angular velocity. That means that stars pass in and out of spiral arms, with stars near the galactic core orbiting faster than the arms are moving while stars near the outer parts of the galaxy typically orbit more slowly than the arms. The spiral arms are thought to be areas of high density matter, or "density waves". As stars move through an arm, the space velocity of each stellar system is modified by the gravitational force of the higher density. (The velocity returns to normal after the stars depart on the other side of the arm.) This effect is akin to a "wave" of slowdowns moving along a highway full of moving cars. The

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arms are visible because the high density facilitates star formation, and therefore they harbor many bright and young stars.

A majority of spiral galaxies have a linear, bar-shaped band of stars that extends outward to either side of the core, and then merges into the spiral arm structure. In the Hubble classification scheme, these are designated by an SB, followed by a lower-case letter (a, b or c) that indicates the form of the spiral arms (in the same manner as the categorization of normal spiral galaxies). Bars are thought to be temporary structures that can occur as a result of a density wave radiating outward from the core, or else due to a tidal interaction with another galaxy. Many barred spiral galaxies are active, possibly as a result of gas being channeled into the core along the arms. Our own galaxy is a large disk-shaped barred-spiral galaxy about 30 kiloparsecs in diameter and a kiloparsec in thickness. It contains about two hundred billion (2×1011) stars and has a total mass of about six hundred billion (6×1011) times the mass of the Sun.

4. Irregular Galaxies

A few percent of the brightest appearing galaxies in the northern sky are the irregular galaxies; these galaxies so no trace of circular or rotational symmetry but have an irregular or chaotic appearance. They are divided into two groups Irr I galaxies, consist of the objects showing high resolution into O and B stars and emission nebulae. The best known examples are the large and small clouds of Magellan (Figure 8.18), our nearest galaxian neighbor. There are many star clusters in these galaxies along with variable stars, supergiants and gaseous nebulae. They contain both old and young stars. The lack of conspicuous dust clouds is common in this first kind of irregular galaxy.

The second irregular type IrrII galaxies resemble IrrI type objects in their lack of symmetry. These objects display no resolution into stars or clusters, but are completely amorphous in texture. Their spectra are continuous with absorption lines and

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resemble the spectra of type A5 stars, showing that the stars in these galaxies are not luminous enough to be resolved. The IrrII galaxies generally also show conspicuous dark lines of absorbing interstellar dust examples are M82 (Figure 8.19) and the companion to the spiral galaxy M51 (Figure 8.20).

Figure 8.18 Large Cloud of Magellian.

Figure 8.19 NGC 3034 (M82) an irregular II galaxy in Ursa Major.

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Figure 8.20 The Sc galaxy NGC 5194 (M51) and its irregular companion NGC 5195

8.4 Classification of galaxies

There have been many classification schemes proposed for galaxies. Among them, one of the earliest, the simplest. And the most used scheme was invented by Hubble during his studies of galaxies in 1920s It consisted of three principal classification sequences elliptical, spiral and barred spirals while the irregular galaxies (IrrI and IrrII) forms a fourth class of object in this classification

Figure 8.21 Types of galaxies according to the Hubble classification scheme. An E indicates a type of elliptical galaxy; an S is a spiral; and SB is a barred-spiral galaxy

The ellipticals are classified according to their degree of flattening or ellipticity. Hubble denoted the spherical galaxies by E0 and most highly flattened by E7. The classes E1, E2, -------- E6 are used for

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galaxies of intermediate ellipticity with each of the number 0 to 7 that describes the flattening of the galaxies is defined in the terms of the major and minor axes of the images of the galaxies, a & b respectively by 10(a-b)/a. Hubble classification of the elliptical galaxies are based on appearance of their images and not upon their true shapes. An E7 galaxy for example, must really be a relatively flat elliptical galaxy seen nearly edge on, but an E0 galaxy could be one of any degree of ellipticity seen face on. A statistical analysis of the number of galaxies of various apparent flattening indicates that if the elliptical galaxies are oblate(like pumpkin) and not prolate (like a football) then all degree of real flattening are about equally represented.

Hubble classified the normal spirals as S and the barred spirals as SB. Lower case letters a, b and c are added to denote the extend of nucleus and the tightness through which the spiral arms are called For example, Sa and SBa galaxies are spirals and barred spirals in which the nuclei are large and arms tightly wound. Sc and SBc are the spirals of opposite extreme. Our Galaxy and M31 are classed as Sb. In rich clusters, galaxies are observed which have the disk shape of spiral but no trace of spiral arm. Hubble classified these galaxies of the type intermediate between spirals and ellipticals and named them S0. Hubble classification scheme for all but irregular galaxies is illustrated in Figure 8.21 in which the morphological form are sketched and labeled and with the three principal sequences joined at S0.

The Hubble classification scheme has been modified and expanded since his time to give a more complete description of galaxies. There are also some of the unusual galaxies as defined below.

cD GALAXIES The cD galaxies are the supergiant elliptical galaxies usually E0 or E1 that are frequently found in (or near) the center of the cluster of galaxies. They are the largest galaxies known and tend to outshine the next brightest cluster galaxies by as much as a factor of 2. They are also a strong radio source.

COMPACT GALAXIES The class of compact galaxies consist of large number of galaxies of relatively small size and high surface brightness; they are usually elliptical or irregular.

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N GALAXIES It is a galaxy with a very bright, nearly stellar appearing nucleus. The rest of galaxy appears as a star of joint, extended haze. Today N galaxies are regarded as belonging to a class of galaxies with active nuclei.

SEYFERT GALAXIES Almost a dozen of galaxies of this class were described by Seyfert, from whom the class derived its name. A Seyfert galaxy is a spiral that has a small bright region in its nucleus whose spectrum shows broad bright emission lines arising from the gases there. They are sometimes strong radio emitters and may be source of very high cosmic rays.

8.5 Other morphologies

Figure 8.22 Hoag's Object, an example of a ring galaxy.

Peculiar galaxies are galactic formations that develop unusual properties due to tidal interactions with other galaxies. An example of this is the ring galaxy, which possesses a ring-like structure of stars and interstellar medium surrounding a bare core. A ring galaxy is thought to occur when a smaller galaxy passes through the core of a spiral galaxy. Such an event may have affected the Andromeda Galaxy, as it displays a multi-ring-like structure when viewed in infrared radiation. A lenticular galaxy is an intermediate form that has properties of both elliptical and spiral galaxies. These are categorized as Hubble type S0, and they possess ill-defined spiral arms with an elliptical halo of stars. (Barred lenticular galaxies receive Hubble classification SB0.)

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Figure 8.23 NGC 5866, an example of a lenticular galaxy..

Dwarf galaxy

Despite the prominence of large elliptical and spiral galaxies, most galaxies in the universe appear to be dwarf galaxies. These tiny galaxies are about one hundredth the size of the Milky Way, containing only a few billion stars. Ultra-compact dwarf galaxies have recently been discovered that are only 100 parsecs across. Many dwarf galaxies may orbit a single larger galaxy; the Milky Way has at least a dozen such satellites, with an estimated 300–500 yet to be discovered. Dwarf galaxies may also be classified as elliptical, spiral, or irregular. Since small dwarf ellipticals bear little resemblance to large ellipticals, they are often called dwarf spheroidal galaxies instead. A study of 27 Milky Way neighbors found that dwarf galaxies were all approximately 10 million solar masses, regardless of whether they have thousands or millions of stars. This has led to the suggestion that galaxies are largely formed by dark matter, and that the minimum size may indicate a form of warm dark matter incapable of gravitational coalescence on a smaller scale.

Interacting galaxy

The average separation between galaxies within a cluster is a little over an order of magnitude larger than their diameter. Hence interactions between these galaxies are relatively frequent, and play an important role in their evolution. Near misses between galaxies

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result in warping distortions due to tidal interactions, and may cause some exchange of gas and dust.

Figure 8.24 The Antennae Galaxies are undergoing a collision that will result in their eventual merger.

Collisions occur when two galaxies pass directly through each other and have sufficient relative momentum not to merge. The stars within these interacting galaxies will typically pass straight through without colliding. However, the gas and dust within the two forms will interact. This can trigger bursts of star formation as the interstellar medium becomes disrupted and compressed. A collision can severely distort the shape of one or both galaxies, forming bars, rings or tail-like structures. At the extreme of interactions are galactic mergers. In this case the relative momentum of the two galaxies is insufficient to allow the galaxies to pass through each other. Instead, they gradually merge together to form a single, larger galaxy. Mergers can result in significant changes to morphology, as compared to the original galaxies. In the case where one of the galaxies is much more massive, however, the result is known as cannibalism. In this case the larger galaxy will remain relatively undisturbed by the merger, while the smaller galaxy is torn apart. The Milky Way galaxy is currently in the process of cannibalizing the Sagittarius Dwarf Elliptical Galaxy and the Canis Major Dwarf Galaxy.

Starburst galaxy

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Figure 8.25 M82, the archetype starburst galaxy, has experienced a 10-fold increase in star formation rate as compared to a "normal" galaxy.

Stars are created within galaxies from a reserve of cold gas that forms into giant molecular clouds. Some galaxies have been observed to form stars at an exceptional rate, known as a starburst. Should they continue to do so, however, they would consume their reserve of gas in a time frame lower than the lifespan of the galaxy. Hence starburst activity usually lasts for only about ten million years, a relatively brief period in the history of a galaxy. Starburst galaxies were more common during the early history of the universe, and, at present, still contribute an estimated 15% to the total star production rate. Starburst galaxies are characterized by dusty concentrations of gas and the appearance of newly formed stars, including massive stars that ionize the surrounding clouds to create H II regions. These massive stars also produce supernova explosions, resulting in expanding remnants that interact powerfully with the surrounding gas. These outbursts trigger a chain reaction of star building that spreads throughout the gaseous region. Only when the available gas is nearly consumed or dispersed does the starburst activity come to an end. Starbursts are often associated with merging or interacting galaxies. The prototype example of such a starburst-forming interaction is M82, which experienced a close encounter with the larger M81. Irregular galaxies often exhibit spaced knots of starburst activity.

8.6 Active galactic nucleus

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A portion of the galaxies we can observe are classified as active. That is, a significant portion of the total energy output from the galaxy is emitted by a source other than the stars, dust and interstellar medium. The standard model for an active galactic nucleus is based upon an accretion disc that forms around a supermassive black hole (SMBH) at the core region. The radiation from an active galactic nucleus results from the gravitational energy of matter as it falls toward the black hole from the disc. In about 10% of these objects, a diametrically opposed pair of energetic jets ejects particles from the core at velocities close to the speed of light. The mechanism for producing these jets is still not well understood.

Figure 8.26 A jet of particles is being emitted from the core of the elliptical radio galaxy M87.

Active galaxies that emit high-energy radiation in the form of x-rays are classified as Seyfert galaxies or quasars, depending on the luminosity. Blazars are believed to be an active galaxy with a relativistic jet that is pointed in the direction of the Earth. A radio galaxy emits radio frequencies from relativistic jets. A unified model of these types of active galaxies explains their differences based on the viewing angle of the observer. Possibly related to active galactic nuclei (as well as starburst regions) are low-ionization nuclear emission-line regions (LINERs). The emission from LINER-type galaxies is dominated by weakly ionized elements. Approximately one-third of nearby galaxies are classified as containing LINER nuclei.

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Our Galaxy has a nucleus that displays many properties similar to that of a quasar, like synchrotron radiations at all wavelengths, infrared radiation and gas clouds moving outward. These phenomenons are on very small scale in our Galaxy when compared with quasars. However, there are galaxies where nuclear activity seems to be intermediate and they may provide a link between normal galaxies and quasars. In 1944, Carl Seyfert described about dozen spiral galaxies with very unusual spectra. The spectrum of the light from the nucleus of a Seyfert galaxy have a strong broad emission lines, which indicates the presence of very hot gas in a small central region . The broad width of the lines shows that the gas is rapidly expanding with the speeds of upto thousands of Km/s. Some of the Seyfert galaxies are also strong radio sources and all have emission of infrared emission from their nuclei. The visual luminosities of these galaxies are usually about normal for spirals, but when account is taken of the infrared energy they emit, their total luminosities are found to be 100 or so times normal. Some are known X-ray source as well.

The unusual radiations from these galaxies sometimes come from several different regions of its nuclei. Some of them like NGC 4151 (Figure 8.27) show the variation in brightness of their nuclei over period of only few months, which is the evidence that the radiation come from small regions at most few light months across. It is possible that 1 or 2 percent of all spiral galaxies have active nuclei.

8.7 Violent Activities in Galaxies

Besides Seyfert galaxies the other galaxies other galaxies show evidence of explosive ejection of matter from the nucleus of M82 (Figure 8.28) with a complex filament surrounding it. The spectra of the filament show Doppler shift suggesting that expansion of upto 1000 Km/s. If they were ejected from the nucleus of M82, they would have their present location in about 2 x 106 years, similar interesting galaxy is M87. It is a strong radio source; short exposures of it show a luminous jet directed away from its nucleus and a faint hint of second radial jet in opposite direction. Both the nucleus and brighter jet emit synchrotron radiation, indicating magnetic fields and a source of relativistic electrons. It is also a strong source of x-rays implying a hot gas throughout the entire galaxy and out into the halo. The

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observation suggests that a halo contains an enormous amount of dark mass perhaps more than 1019 solar mass. Finally, the optical spectrum of M87 show very broad lines indicating very high velocities of stars there, as though they were being accelerated by a very dense, massive core. Between quasars and galaxies like M82 and M87 or Seyfert galaxies there is another class called N-galaxies having small nuclei that are very bright compared with the main part of these galaxies appear as stellar images superposed on joint wispy or nebulous backgrounds. Their bright nuclei indicate that enormous amount of energy being emitted from those regions.

Figure 8.27 Seyfert galaxy NGC 41251

Figure 8.28 M82

8.8 Power House of Active Galactic Nuclei

The source of energy of Active Galactic Nuclei is required to have some of the following properties.

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It must provide power upto 1047 ergs/s equivalent to nearly 100 million million times the luminosity of the sun.

It must in some cases account for the variation in the total radiated power by as much as a factor of two or more and over time scales of years or months or in some cased only days.

In the objects that vary in luminosity, the powerhouse must be compact enough that light can travel across it in a time less than that of its variations.

It must be able to eject relativistic electrons in directed jets and in sufficient numbers to provide synchrotron radiation as intense as the total visible energy emitted by bright galaxy.

It must possess powerful magnetism and the energy in the magnetic fields must be comparable to the total nuclear energy available in all of the stars in a large galaxy.

At least in M87 and probably in many galaxies it must be able to accelerate the stars to high velocities in central regions of the galaxy in which they reside.

In some quasars it must be able to eject clouds of matter containing relativistic electrons every year or more often.

Perhaps no one kind of power plant accounts for all kind of active galactic nuclei, but what they all have in common points to a small compact source of enormous energy, evidently buried in the nucleus of the galaxy. Many models have been suggested, including stellar collisions in dense galactic cores, superstars, extraordinary powerful supernovae, and others. But most of the theoreticians lean to the theory that all or most active galactic nuclei derives their energy from the release of potential energy in the gravitational collapse of millions or thousands of millions of solar masses. This matter, falling together and accelerating as it goes so, would reach great speeds and the heat to millions of Kelvin. Ultimately, it is believed such collapsing matter must increase the density until it has fallen through its event horizon into a black hole. New matter, falling towards black hole, release new energy and probably forms accretion disk. Perhaps the ejection of jets of matter in radio galaxies and quasars is large scale

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version of SS433. These ideas are of course speculative, we know we have small compact source of enormous energy, and it seems reasonable to suppose it to be associated with something like black hole, but no one model has achieved anything close to universal acceptance

8.9 Galaxy formation and evolution

The study of galactic formation and evolution attempts to answer questions regarding how galaxies formed and their evolutionary path over the history of the universe. Some theories in this field have now become widely accepted, but it is still an active area in astrophysics.

Figure 8.29 Formation of galaxies

1. Formation

Current cosmological models of the early Universe are based on the Big Bang theory. About 300,000 years after this event, atoms of hydrogen and helium began to form, in an event called recombination. Nearly all the hydrogen was neutral (non-ionized) and readily absorbed light, and no stars had yet formed. As a result this period has been called the "Dark Ages". It was from density fluctuations (or anisotropic irregularities) in this primordial matter that larger structures began to appear. As a result, masses of baryonic matter started to condense within cold dark matter halos. These primordial structures would eventually become the galaxies we see today.

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Evidence for the early appearance of galaxies was found in 2006, when it was discovered that the galaxy IOK-1 has an unusually high redshift of 6.96, corresponding to just 750 million years after the Big Bang and making it the most distant and primordial galaxy yet seen. While some scientists have claimed other objects (such as Abell 1835 IR1916) have higher redshifts (and therefore are seen in an earlier stage of the Universe's evolution), IOK-1's age and composition have been more reliably established. The existence of such early protogalaxies suggests that they must have grown in the so-called "Dark Ages”. The detailed process by which such early galaxy formation occurred is a major open question in astronomy. Theories could be divided into two categories: top-down (or Outside – In) and bottom-up (or Inside – Out). In top-down theories protogalaxies are form in a large-scale simultaneous collapse lasting about one hundred million years. In bottom-up theories small structures such as globular clusters form first, and then a number of such bodies accrete to form a larger galaxy. Modern theories must be modified to account for the probable presence of large dark matter halos.

Once protogalaxies began to form and contract, the first halo stars (called Population III stars) appeared within them. These were composed almost entirely of hydrogen and helium, and may have been massive. If so, these huge stars would have quickly consumed their supply of fuel and became supernovae, releasing heavy elements into the interstellar medium. This first generation of stars re-ionized the surrounding neutral hydrogen, creating expanding bubbles of space through which light could readily travel.

2, Evolution

Within a billion years of a galaxy's formation, key structures begin to appear. Globular clusters, the central supermassive black hole, and a galactic bulge of metal-poor Population II stars form. The creation of a supermassive black hole appears to play a key role in actively regulating the growth of galaxies by limiting the total amount of additional matter added. During this early epoch, galaxies undergo a major burst of star formation. During the following two billion years, the accumulated matter settles into a galactic disc. A galaxy will continue to absorb infalling material from high velocity clouds and dwarf galaxies throughout its life. This matter is mostly hydrogen and

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helium. The cycle of stellar birth and death slowly increases the abundance of heavy elements, eventually allowing the formation of planets.

Figure 8.30 I Zwicky 18 (lower left) resemble a newly formed galaxy.

The evolution of galaxies can be significantly affected by interactions and collisions. Mergers of galaxies were common during the early epoch, and the majority of galaxies were peculiar in morphology. Given the distances between the stars, the great majority of stellar systems in colliding galaxies will be unaffected. However, gravitational stripping of the interstellar gas and dust that makes up the spiral arms produces a long train of stars known as tidal tails. Examples of these formations can be seen in NGC 4676 or the Antennae Galaxies. As an example of such an interaction, the Milky Way galaxy and the nearby Andromeda Galaxy are moving toward each other at about 130 km /s and— depending upon the lateral movements—the two may collide in about five to six billion years. Although the Milky Way has never collided with a galaxy as large as Andromeda before, evidence of past collisions of the Milky Way with smaller dwarf galaxies is increasing. Such large-scale interactions are rare. As time passes, mergers of two systems of equal size become less common. Most bright galaxies have remained fundamentally unchanged for the last few billion years, and the net rate of star formation probably also peaked approximately ten billion years ago.

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Future trends

At present, most star formation occurs in smaller galaxies where cool gas is not so depleted. Spiral galaxies, like the Milky Way, only produce new generations of stars as long as they have dense molecular clouds of interstellar hydrogen in their spiral arms. Elliptical galaxies are already largely devoid of this gas, and so form no new stars. The supply of star-forming material is finite; once stars have converted the available supply of hydrogen into heavier elements, new star formation will come to an end. The current era of star formation is expected to continue for up to one hundred billion years, and then the "stellar age" will wind down after about ten trillion to one hundred trillion years (1013–1014 years), as the smallest, longest-lived stars in our astrosphere, tiny red dwarfs, begin to fade. At the end of the stellar age, galaxies will be composed of compact objects: brown dwarfs, white dwarfs that are cooling or cold ("black dwarfs"), neutron stars, and black holes. Eventually, as a result of gravitational relaxation, all stars will either fall into central supermassive black holes or be flung into intergalactic space as a result of collisions.

8.10 Large-scale structure of the cosmos and Groups and clusters of galaxies

There are probably more than 100 billion (1011) galaxies in the observable universe. Most galaxies are 1,000 to 100,000 parsecs in diameter and are usually separated by distances on the order of millions of parsecs (or megaparsecs). Intergalactic space (the space between galaxies) is filled with a tenuous gas of an average density less than one atom per cubic meter. The majority of galaxies are organized into a hierarchy of associations called clusters, which, in turn, can form larger groups called superclusters. These larger structures are generally arranged into sheets and filaments, which surround immense voids in the universe,

Deep sky surveys show that galaxies are often found in relatively close association with other galaxies. Solitary galaxies that have not significantly interacted with another galaxy of comparable mass during the past billion years are relatively scarce. Only about 5% of the galaxies surveyed have been found to be truly isolated; however, these isolated formations may have interacted and even merged with

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other galaxies in the past, and may still be orbited by smaller, satellite galaxies. Isolated galaxies can produce stars at a higher rate than normal, as their gas is not being stripped by other, nearby galaxies. On the largest scale, the universe is continually expanding, resulting in an average increase in the separation between individual galaxies (see Hubble's law). Associations of galaxies can overcome this expansion on a local scale through their mutual gravitational attraction. These associations formed early in the universe, as clumps of dark matter pulled their respective galaxies together. Nearby groups later merged to form larger-scale clusters. This on-going merger process (as well as an influx of infalling gas) heats the inter-galactic gas within a cluster to very high temperatures, reaching 30–100 million K. About 70–80% of the mass in a cluster is in the form of dark matter, with 10–30% consisting of this heated gas and the remaining few percent of the matter in the form of galaxies.

Figure 8.31 Seyfert's Sextet is an example of a compact galaxy group.

Most galaxies in the universe are gravitationally bound to a number of other galaxies. These form a fractal-like hierarchy of clustered structures, with the smallest such associations being termed groups. A group of galaxies is the most common type of galactic cluster, and these formations contain a majority of the galaxies (as well as most of the baryonic mass) in the universe. To remain gravitationally bound to such a group, each member galaxy must have a sufficiently low velocity to prevent it from escaping. If there is insufficient kinetic energy, however, the group may evolve into a smaller number of

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galaxies through mergers. Larger structures containing many thousands of galaxies packed into an area a few megaparsecs across are called clusters. Clusters of galaxies are often dominated by a single giant elliptical galaxy, known as the brightest cluster galaxy, which, over time, tidally destroys its satellite galaxies and adds their mass to its own. Superclusters contain tens of thousands of galaxies, which are found in clusters, groups and sometimes individually. At the supercluster scale, galaxies are arranged into sheets and filaments surrounding vast empty voids. Above this scale, the universe appears to be isotropic and homogeneous. The Milky Way galaxy is a member of an association named the Local Group, a relatively small group of galaxies that has a diameter of approximately one megaparsec. The Milky Way and the Andromeda Galaxy are the two brightest galaxies within the group; many of the other member galaxies are dwarf companions of these two galaxies. The Local Group itself is a part of a cloud-like structure within the Virgo Supercluster, a large, extended structure of groups and clusters of galaxies centered on the Virgo Cluster.

8.11 Modern research

Figure 8.32 Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The distance is from the galactic core.

In 1944 Hendrik van de Hulst predicted microwave radiation at a wavelength of 21 cm resulting from interstellar atomic hydrogen gas; this radiation was observed in 1951. The radiation allowed for much improved study of the Milky Way Galaxy, since it is not affected by dust absorption and its Doppler shift can be used to map the motion of the gas in the Galaxy. These observations led to the postulation of

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a rotating bar structure in the center of the Galaxy. With improved radio telescopes, hydrogen gas could also be traced in other galaxies.

In the 1970s it was discovered in Vera Rubin's study of the rotation speed of gas in galaxies that the total visible mass (from the stars and gas) does not properly account for the speed of the rotating gas. This galaxy rotation problem is thought to be explained by the presence of large quantities of unseen dark matter. Beginning in the 1990s, the Hubble Space Telescope yielded improved observations. Among other things, it established that the missing dark matter in our galaxy cannot solely consist of inherently faint and small stars. The Hubble Deep Field, an extremely long exposure of a relatively empty part of the sky, provided evidence that there are about 125 billion (1.25×1011) galaxies in the universe. Improved technology in detecting the spectra invisible to humans (radio telescopes, infrared cameras, and x-ray telescopes) allow detection of other galaxies that are not detected by Hubble. Particularly, galaxy surveys in the zone of avoidance (the region of the sky blocked by the Milky Way) have revealed a number of new galaxies.

8.12 Multi-wavelength observation

After galaxies external to the Milky Way were found to exist, initial observations were made mostly using visible light. The peak radiation of most stars lies here, so the observation of the stars that form galaxies has been a major component of optical astronomy. It is also a favorable portion of the spectrum for observing ionized H II regions, and for examining the distribution of dusty arms.

The dust present in the interstellar medium is opaque to visual light. It is more transparent to far-infrared, which can be used to observe the interior regions of giant molecular clouds and galactic cores in great detail. Infrared is also used to observe distant, red-shifted galaxies that were formed much earlier in the history of the universe. Water vapor and carbon dioxide absorb a number of useful portions of the infrared spectrum, so high-altitude or space-based telescopes are used for infrared astronomy.

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The first non-visual study of galaxies, particularly active galaxies, was made using radio frequencies. The atmosphere is nearly transparent to radio between 5 MHz and 30 GHz. (The ionosphere blocks signals below this range.) Large radio interferometers have been used to map the active jets emitted from active nuclei. Radio telescopes can also be used to observe neutral hydrogen (via 21 centimeter radiation), including, potentially, the non-ionized matter in the early universe that later collapsed to form galaxies. Ultraviolet and X-ray telescopes can observe highly energetic galactic phenomena. An ultraviolet flare was observed when a star in a distant galaxy was torn apart from the tidal forces of a black hole. The distribution of hot gas in galactic clusters can be mapped by X-rays. The existence of super-massive black holes at the cores of galaxies was confirmed through X-ray astronomy.

Although it is not yet well understood, dark matter appears to account for around 90% of the mass of most galaxies. Observational data suggests that supermassive black holes may exist at the center of many, if not all, galaxies. They are proposed to be the primary cause of active galactic nuclei found at the core of some galaxies. The Milky Way galaxy appears to harbor at least one such objects within its nucleus.

8.13 Quasars

If we consider the sun as typical among stars to be a radio emitter, we would not expect to be able to observe a single other star at radio wavelengths, the radio emission from the stars would be too feeble to detect with existing instruments. It was with considerable surprise that in 1960 two radio sources was identified with what appear to be stars. There seems to be no chance that the identifications were in error because the precise position of the radio sources was pinned down by noting the exact instants they were occulted by the moon. By 1963 the number of such “radio stars” has increased to four. They were especially perplexing objects because their optical spectra showed emission lines that at first could not be identified known chemical elements.

The real breakthrough came in 1963, when M Smidth, at Caltech’s Palomar observatory recognized the emission lines in one of the

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object to be Balmer lines of hydrogen shifted far to the red from their normal wavelengths. If the redshift are the Doppler shift then the object must be receding from us at about 15 percent the speed of light. With this hint, the emission lines in other objects were reexamined to see if they too might be well known lines with large redshifts, such proved, indeed to be the case, but the other objects were found to be receding from us even at greater speeds. Thus they could be not our neighboring stars; their stellar appearance might be due to the fact that they are very distant. They are therefore called Quasi-Stellar-Radio–Sources or simply Quasi-Stellar Sources (abbreviated QSS). Later similar objects found were not the sources of strong radio emissions. Today they all are designated by the term QUASAR. The discovery of these peculiar objects prompted the search for the others. A modern procedure is to look for stellar appearing object at the position of unidentified radio sources or to examine stellar appearing images of peculiar blue color. By 1980 hundreds of quasars had been catalogued and systematic survey indicates that there must be more than 20,000 brighter than 18 magnitudes. The number of still fainter is not known but they must be many. All have the spectra that show large to very large redshifts. The relative shifts of wavelength range upto Δ λ/ λ = 3.53 corresponds to velocity of recession of 91 percent of the speed of light. Most investigators regarded the redshifts of the distances and that they confirmed to the Hubble Law. The quasars have very much higher speeds than any known galaxy and must be even more distant.

8.14 Characteristics

The quasars are unresolved optically, that is, they appear stellar and most of them as very faint stars 3C273 (Figure 8.32 37.29) is still several hundred times too faint to see with the unaided eye. Few quasars are associated with tiny wisps of filaments of nuclear appearing matter. Some are resolved at radio wavelengths, which indicate that the radio energy come from region outside the photographic images as found for the radio radiation from galaxies that often originates from outside their optical images. The radio radiation is believed to be synchrotron. Quasars differ considerably from each other in luminosity. They are extremely luminous at all wavelengths. In radio energy they are as bright as brightest radio

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galaxies and in visible light most are far more luminous than the brightest elliptical galaxies. They have absolute magnitude in the range -25 or -26 and are very blue in color. In fact, one of those recognizable characteristics is their excess amount of their ultraviolet radiation, compared with normal star and galaxies. Most surprising of all is that almost all of them are variable both in radio emission and visible range. There variations are irregular evidently at random by few tenths of magnitude or so, but some times flare-ups of more than a magnitude are observed in an interval of few weeks. Since the quasars are highly luminous a change in brightness by a magnitude (a factor of 2.5 in light) means extremely great amount of energy is released rather suddenly. Further, as the fluctuations occur in such short times, the part of quasar responsible for light and radio variations must be smaller than the distance light travels in a month or so, otherwise the light emitted at one time from different parts of the objects would reach the earth at different times and we would see the increased spread over long time.

Figure 8.32 Quasi-stellar radio sources.

8.15 Double Quasar 0957 + 561: A gravitational Lens

In 1979 astronomers, D. Walsh, R.F. Carswell, and R.J. Weymenn observed a pair of Quasars separated by only 6” and are collectively known as 0957+561 the numbers representing their coordinates in

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the sky. They were remarkably similar in the appearance and spectra. They both are about 17 magnitude and both have the redshift (Δλ/λ) of 1.4. The astronomers suggested two quasars might actually be one, and we are seeing two images produced by inverting object acting as gravitational lens. In 1980 team of astronomers at Palomar found an 18th magnitude galaxy next to one of the quasar. In fact, the galaxy turns out to be member of cluster of galaxies with the redshift of 0.39. The geometry and the estimated mass of the galaxies are correct to produce the gravitational lens effect. A schematic of the lens is shown in Figure 8.33 and Figure 8.34

Figure 8.33 Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

Figure 8.34 Schematic of Gravitational lens

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Summery

1. A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants,

2. Actual proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is composed of a huge number of faint stars.

3. A very significant contribution to our knowledge of the galaxies was provides by the work of William Herschel and his only son, John (1792-1871).

4. the word Universe was understood to mean the entirety of existence

5. Typical galaxies range from dwarfs with as few as ten million (107) stars up to giants with one trillion (1012) stars, all orbiting the galaxy's center of mass

6. Galaxies can also contain many multiple star systems, star clusters, and various interstellar clouds.

7. elliptical galaxies are spherical ellipsoidal system that is thought to consist almost entirely of old stars

8. A spiral galaxy consists of a nucleus, a disk, a halo and the spiral arm

9. A large minority of spiral galaxies display “bars” running through nuclei

10. Spiral galaxies consist of a rotating disk of stars and interstellar medium, along with a central bulge of generally older stars

11. Peculiar galaxies are galactic formations that develop unusual properties due to tidal interactions with other galaxies

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12. Theories could be divided into two categories: top-down and bottom-up. In top-down theories protogalaxies are form in a large-scale simultaneous collapse lasting about one hundred million years. In bottom-up theories small structures such as globular clusters form first, and then a number of such bodies accrete to form a larger galaxy.

13. (or Outside –In)

14. The creation of a supermassive black hole appears to play a key role in actively regulating the growth of galaxies by limiting the total amount of additional matter added.

15. The evolution of galaxies can be significantly affected by interactions and collisions. Mergers of galaxies were common during the early epoch, and the majority of galaxies were peculiar in morphology.

16. At present, most star formation occurs in smaller galaxies where cool gas is not so depleted.

17. There are probably more than 100 billion (1011) galaxies in the observable universe.

18. Most galaxies in the universe are gravitationally bound to a number of other galaxies.

Exercises Fill in the blanks1 In 1755 Immanuel Kant introduced the term ___________ for

distant nebulae.2 Typical galaxies range from _________ with as few as ten

million (107) stars up to __________ with one trillion (1012) stars, all orbiting the galaxy's center of mass.

3 The __________is one of the stars in the Milky Way galaxy.4 Galaxies differ a great deal among themselves but majority fall

into two general classes____________ and ____________.5 A minority of galaxies are classed as ___________.

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6 Starburst galaxies are the result of a ___________ collision.7 In spiral galaxies, the spiral arms have the shape of

approximate ___________ spirals.8 Ultra-compact dwarf galaxies have recently been discovered

that are only ____________ across.9 Stars are created within galaxies from a reserve of __________

that forms into giant molecular clouds.10 A portion of the galaxies we can observe are classified as

________.11 Theories of formation of galaxies could be divided into two

categories namely ______________ and _____________.12 Only about ______ of the galaxies surveyed have been found

to be truly isolated.13 _________ matter appears to account for around 90% of the

mass of most galaxies.14 _________ are extremely luminous at all wavelengths.

Short questions with answer

Q1. What is a galaxy?Ans. A galaxy is a massive, gravitationally bound system that

consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy derives from the Greek term for our own galaxy, galaxias "milky circle" for its appearance in the sky.

Q2. When it was proved that Milky Way consists of number of stars?

Ans. Actual proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is composed of a huge number of faint stars.

Q3. What is a nebula?Ans. nebulae (plural of nebula) that literally means “clouds”. Faint

star clusters glowing gas clouds, dust clouds reflecting starlight, and galaxies all appear as joint unresolved luminous patches when viewed visually with the telescopes of only moderate size, Since the true nature of these objects were not known to early observers , all of them were called nebulae. Today we usually reserve the word “nebula” for the true gas or dust clouds, but

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some astronomers still refer to galaxies as nebulae or extragalactic nebulae.

Q4. What is universe?Ans. The word Universe means the entirety of existence.Q5. What were the first galaxies other than the Milky Way to be

observed from Earth?Ans. In the 10th century, the Persian astronomer, Abd al-Rahman al-

Sufi (known in the West as Azophi), made the earliest recorded observation of the Andromeda Galaxy, describing it as a "small cloud". Al-Sufi also identified the Large Magellanic Cloud, which is visible from Yemen, though not from Isfahan; it was not seen by Europeans until Magellan's voyage in the 16th century. These were the first galaxies other than the Milky Way to be observed from Earth.

Q6. What is a galaxy?Ans. A galaxy is a massive, gravitationally bound system that

consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy derives from the Greek term for our own galaxy, galaxias "milky circle" for its appearance in the sky.

Q7. What do you understand by term island universe?Ans. In 1755 Immanuel Kant introduced the term "island universe" in

his hypothesis for distant nebulae which states that spiral nebulae are actually independent galaxies.

Q8. What is the structure of galaxy?Ans. Typical galaxies range from dwarfs with as few as ten million

(107) stars up to giants with one trillion (1012) stars, all orbiting the galaxy's center of mass. Galaxies can also contain many multiple star systems, star clusters, and various interstellar clouds.

Q9. What are the types of galaxy?Ans. Galaxies differ a great deal among themselves but majority fall

into two general classes; ellipticals and spirals; a minority is classed as irregular

Q10. How galaxies are classified?Ans. There have been many classification schemes proposed for

galaxies, among them, one of the earliest, the simplest. And the most used scheme was invented by Hubble during his studies of galaxies in 1920s It consisted of three principal classification

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sequences elliptical, spiral and barred spirals while the irregular galaxies (IrrI and IrrII) forms a fourth class of object in this classification

Q11. What are peculiar galaxies?Ans. Peculiar galaxies are galactic formations that develop unusual

properties due to tidal interactions with other galaxies. An example of this is the ring galaxy, which possesses a ring-like structure of stars and interstellar medium surrounding a bare core, another peculiar galaxy is a lenticular galaxy which is an intermediate form that has properties of both elliptical and spiral galaxies. These are categorized as Hubble type S0, and they possess ill-defined spiral arms with an elliptical halo of stars

Q12. What is the relative prominence galaxy?Ans. Despite the prominence of large elliptical and spiral galaxies,

most galaxies in the universe appear to be dwarf galaxies. These tiny galaxies are about one hundredth the size of the Milky Way; ultra-compact dwarf galaxies that have recently been discovered are only 100 parsecs across.

Q13. What is average separation between galaxies?Ans. The average separation between galaxies within a cluster is a

little over an order of magnitude larger than their diameter. Hence interactions between these galaxies are relatively frequent, and play an important role in their evolution

Q14. What is a Starburst galaxy?Ans. Starburst galaxies are characterized by dusty concentrations of

gas and the appearance of newly formed stars, including massive stars that ionize the surrounding clouds to create H II regions. Starburst galaxies were more common during the early history of the universe, and, at present, still contribute an estimated 15% to the total star production rate.

Q15. What is an active galaxy?Ans. A portion of the galaxies we can observe are classified as

active. That is, a significant portion of the total energy output from the galaxy is emitted by a source other than the stars, dust and interstellar medium.

Q16. What is a Seyfert galaxy?Ans. Active galaxies that emit high-energy radiation in the form of x-

rays are classified as Seyfert galaxies or quasars, depending on the luminosity.

Q17. What are N-galaxies?

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Ans. N-galaxies having small nuclei that are very bright compared with the main part of these galaxies appear as stellar images superposed on joint wispy or nebulous backgrounds. Their bright nuclei indicate that enormous amount of energy being emitted from those regions.

Q18. What are the different processes of the formation of galaxies?Ans. The detailed process by which such early galaxy formation

occurred is a major open question in astronomy. Theories could be divided into two categories: top-down (or outside – In) and bottom-up (or inside – Out). In top-down theories protogalaxies are form in a large-scale simultaneous collapse lasting about one hundred million years. In bottom-up theories small structures such as globular clusters form first, and then a number of such bodies accrete to form a larger galaxy.

Q19. What are the numbers galaxies in the universe? How they are arranged?

Ans. The Hubble Deep Field, an extremely long exposure of a relatively empty part of the sky, provided evidence that there are about 125 billion (1.25×1011) galaxies in observable universe. Most galaxies are 1,000 to 100,000 parsecs in diameter and are usually separated by distances on the order of millions of parsecs (or megaparsecs). The majority of galaxies are organized into a hierarchy of associations called clusters, which, in turn, can form larger groups called superclusters. These larger structures are generally arranged into sheets and filaments, which surround immense voids in the universe.

Study QuestionsQ1. What were the views of the ancients about the Milky Way?Q2. What nebula? How do you differentiate from the galaxy?Q3. What are the typical range of galaxies?Q4. What are different types of galaxies?Q5. Write note on:

Elliptical galaxy Spiral Galaxies Barred spiral galaxy Irregular Galaxies

Q6. Explain the Hubble classification scheme of the galaxies?Q7. Define the unusual galaxies?Q8. What is active galactic nucleus?

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Q9. Discuss the Violent Activities in Galaxies?Q10. Discuss the properties source of energy of Active Galactic

Nuclei?Q11. How the galaxies are formed?Q12. What is the process of the evolution of the galaxies?Q13. What is Quasars? Explain its characteristics?Q14. Discuss the Large-scale structure of the cosmos?Q15. What is gravitational lens?

Creation of Universe

Unit V

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Chapter 9

Albert Einstein  (14 March 1879–18 April 1955) was a German-born Swiss-American theoretical physicist, philosopher and author who is widely regarded as one of the most influential and best known scientists and intellectuals of all time. He is often regarded as the father of

modern physics. He received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."

The Universe

When we look off into space we look back into time for we see remote objects as (and where) they were far in the past, when the light left them to begin its long journey across space to reach our telescopes. Remote objects, therefore in a sense are the historical

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documents in the universe even though we have difficulty in interpreting their meanings.

It is clear that if the stars are in the galaxies, galaxies in the cluster of galaxies and clusters in superclusters, it is natural to wonder whether hierarchy might go on to ever higher orders of clusters of galaxies. The available evidence suggests that it does not because. First, if it did, it would never be possible to define a region of space beyond which the universe is homogeneous because large hierarchal structures would always exist. This would violet the cosmological principle as against the observations.

Further the superclusters appear to expanding and the meager evidence suggests that most are not gravitationally bound. If superclusters are not gravitationally bound, the next order cluster should expand more rapidly and the order beyond them more so yet. It is hard to see how this hierarchal structure be maintained. Research by George Rainey has ruled out the inhomogeneites in a scale as large as 500 million parsecs. This indicates that there cannot be “super-duper” cluster. Moreover, faint background of radio radiations that we interpret as dying glow of big bang that started the expansion of the universe suggest that uniformity of the radiation in different directions is impressive and argues for higher high degree of homogeneity in the universe at large.

Most or all the matter of the universe appears to be clustered in the system of size upto at least 300 million light years-superclusters, but on very large scale the universe is very uniform which rules out the hierarchal distribution of matter in space. However, the future of the universe depends critically on mean density of the matter in space. Since it would add to the mass and hence the gravitation of the universe, but not to the light. If such matter was concentrated in the cluster of galaxies, it could account for their, perhaps high mass to light ratios. But the total mass of such matter in the universe would nevertheless already be tallied, for it is included in the masses we drive for clusters. One of the possible candidates for the dark matter in the universe if it exists is neutrinos. In fact, they should turn out to have non zero rest mass. If they are distributed uniformly throughout the universe, it is estimated that at present each square centimeter contains several hundred neutrinos, originally produced in big bang, If

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they should have no rest mass, or very small rest mass, neutrinos are expected to be distributed uniformly. A neutrino would have to have a mass as much as 2 x 10‾6 times that of electron to contribute to the density of the universe enough to effect its evolution and if they should have very tiny rest mass neutrinos would probably clump with clusters or superclusters of galaxies. Here we should point out that the evidence for neutrinos having mass is only suggestive, but even if this suggestion is correct, neutrinos probably cannot be important in overall gravitation of the universe. They could however, play an important role in resolving high mass to light ratio anomalies in galaxies and clusters. The theory of large scale structure, which governs the formation of structure in the universe stars, quasars, galaxies and galaxy clusters, also suggests that the density of baryonic matter in the universe is only 30% of the critical density.

9.1 Nature of dark energy

The term "dark energy" was coined by Michael Turner in 1998, a term similar to Fritz Zwicky's "Dark Matter" coined in the 1930's. By that time, the missing mass problem of big bang nucleosynthesis and large scale structure was established, and some cosmologists had started to theorize that there was an additional component to our universe. The first direct evidence for dark energy came from supernova observations of accelerated expansion.

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Figure 9.1 Dark Energy

Figure 9.2 Dark Matter

In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be expanding at an accelerating. In the standard model of cosmology, dark energy currently accounts for 74% of the total mass-energy of the universe.

Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously, and scalar fields such as quintessence or moduli, dynamic quantities whose

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energy density can vary in time and space. Contributions from scalar fields that are constant in space are usually also included in the cosmological constant. The cosmological constant is physically equivalent to vacuum energy. Scalar fields which do change in space can be difficult to distinguish from a cosmological constant because the change may be extremely slow.

The exact nature of this dark energy is a matter of speculation. It is known to be very homogeneous, not very dense and is not known to interact through any of the fundamental forces other than gravity. Since it is not very dense — roughly 10−29 grams per cubic centimeter — it is hard to imagine experiments to detect it in the laboratory. Dark energy can only have such a profound impact on the universe, making up 74% of universal density, because it uniformly fills otherwise empty space. The two leading models are quintessence and the cosmological constant. Both models include the common characteristic that dark energy must have negative pressure.

9.2 Negative pressure

Independently from its actual nature, dark energy would need to have a strong negative pressure in order to explain the observed acceleration in the expansion rate of the universe.

According to General Relativity, the pressure within a substance contributes to its gravitational attraction for other things just as its mass density does. This happens because the physical quantity that causes matter to generate gravitational effects is the Stress-energy tensor, which contains both the energy (or matter) density of a substance and its pressure and viscosity. It can be shown that a strong constant negative pressure in the entire universe causes acceleration in universe expansion if the universe is already expanding or a deceleration in universe contraction if the universe is already contracting.

This accelerating expansion effect is sometimes labeled "gravitational repulsion", which is a colorful but possibly confusing expression. In fact a negative pressure does not influence the gravitational interaction between masses - which remains attractive - but rather

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alters the overall evolution of the universe at the cosmological scale, typically resulting in the accelerating expansion of the universe despite the attraction among the masses present in the universe.

9.3 The Beginning of Universe

The specific model for the big bang was first proposed by George Lemaitre. He envisioned all the matter of the universe starting in one great bulk he called the primeval atom. It broke into tremendous number of pieces, each of them further fragmenting and so on until what were left were the present atoms of the universe, created in vast nuclear fission. Today we know much more about nuclear physics and that primeval fission model cannot be correct, yet Lemarite’s vision inspired more modern work.

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Figure 9.3 Time Line for Big Bang

9.4 Standard Model for Big Bang

The modern theory of the evolution of early universe is called the standard model of the big bang details of which were worked out in 1967 by Robert Wagoner at Stanford university and William Fowler and Fred Hoyle at Caltech. In first tiny fraction of second, it is thought that all kinds of particles existed in equilibrium with radiation-particles and their antiparticles being produced in pair from photons and annihilating reconverting to photons again. By the time the universe was one second old, it would have cooled to about 10¹º K, by which time the prevalent photons were not of high enough energy to create pairs of particles. Then the matter consisted of particles such as protons, electrons, positrons and neutrons and neutrinos. By the time the universe was 100 s old, the temperature has dropped to 109 K and the particles began to combine to form heavier nuclei, this neucleosynthesis continued for next few minutes during which about 25 percent of the mass of the material formed into helium. Some deuterium was also formed but only a small amount probably less than one part in ten thousand. The actual amount of the deuterium formed depends critically on the density of the fireball, if it was fairly high, most of the deuterium would have been built up into helium. Scarcely any nuclei heavier than those of helium are expected to have survived so the composition of the fireball when the nuclear building ceased is thought to have been mostly hydrogen, about 25 percent helium and traces of deuterium. It was the striking success of the standard model that the predicted ratio of hydrogen to helium – three to one by mass is just the ratio observed in stars ad interstellar matter. A small enhancement of helium must have resulted from the neucleosynthesis in stars, to be sure, but by far most of the helium must be primordial – especially in the outer layers of the stars. Hence the agreement between prediction and observation must be regarded as a second triumph for the big bang and the relativistic evolving cosmological theories, the first being the expansion of the universe.

For next few hundred thousand years, the fireball was like a stellar interior- hot and opaque with radiation being scattered from one particle to another. By about 700,000 years after the big bang the

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temperature has dropped to about 3000 K and the density of the atomic nuclei to about 1000 per cubic centimeter. Under these conditions, the electrons and nuclei combine to form stable atom of hydrogen and helium. With no free electrons to scatter photons, the universe became transparent, and the matter and radiation no longer interacted subsequently each evolved in its separate way.

One thousand million years after the big bang stars and the galaxies had probably begun to form but we are not sure of the precise mechanisms. Certainly, deep in the interior of star the matter was reheated, star began to shine, nuclear reactions were ignited and the gradual synthesis of the heaver elements began. Now we must point out that the fireball must not be thought of a localized explosion like exploding superstar. There were no boundaries and no site of explosion. It was everywhere. The fireball still exists in a sense. It has expanded greatly but the original matter and radiation are still present and accounted for. The stuff of our bodies comes from the material in the fireball. We were and are still in the midst of it. It is all around us.

9.5 Hubble Expansion Model

In 1931, Hubble and Milton Humason jointly published their classical paper in Astrophysical Journal, which compared the distances and the velocities of remote galaxies moving away from us at so speed up to nearly 20,000 Km/s. Their law of the red shift (Figure 9.4) now known as Hubble Law established the expansion of the universe beyond doubt, even though the authors were cautious about so interpreting their observations.

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Figure 9.4 Hubble and Humason’s velocity distance relation adapted from their 1931 paper in the Astrophysical Journal.

Subsequently more and more remote galaxies of greater and greater speed of recession have been found The cluster of galaxies as shown in the Figure 9.5 moves away from us at the speed of 108,000 Km/s-36 percent of the speed of light. Even more remote clusters have been found, in 1981 Hyron Spinrad at University of California, Berkeley reported the observation of two clusters receding at about 60 percent the speed of light. The relative distances to the clusters are known fairly well, and so the accuracy of the observations, remote cluster of galaxies has velocities that are proportional to their distances. The constant of proportionality, symbolized H and called Hubble constant specifies the rate of recession of galaxies or clusters of various distances. The Hubble constant is now believed to lie in the range 50 to 100 Km/s per million parsecs. If H is 75 Km/s per million parsecs a cluster moves away from us at a speed of 75 Km/s for every million parsecs of its distances. A test of Hubble law involved the speed of receding galaxies at great distances. The evolutionary model predicted the expansion to slow down due to the gravitational forces between galaxies. Because of these changes in the rate of expansion of universe, the radial velocities of remote galaxies would deviate from a relation exactly proportional to their observed distances, that is. The graph of radial velocity versus distance should not necessarily be straight line for very distant galaxies.

Figure 9.5 JKCS 041 is a group of galaxies with the distinction of being the farthest away group from Earth ever observed, as of 2009. It is estimated to be 10.2 billion light years away, seen at redshift

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1.9.The cluster is located at a photometrically determined redshift of z=1.9 at right ascension 2h 26m 44s declination -04° 41′ 37″.

9.6 Cosmic Microwave Background Radiation

It was realized by Alpher and Robert Herman that when the universe became transparent it must have been radiating like a black body at a temperature of 3000 K. If we cold have seen that freed radiations just after the neutral atom were formed, it would have resembled that from a reddish star, but that was at least ten thousand million years ago. In the meantime the scale of universe has increased a thousand fold. The light emitted by once hot gas in our part of the universe is now thousands of millions of light years away. Thus to observe that glow of the early universe, we must look in all directions in space to such great distance-10 to 20 thousand million light year – that we are looking back in time through those 10 to 20 thousand million years. Due to expansion these remote parts of universe should be receding from us at a speed within two parts in a million of that of light. The radiation from them would be Doppler shifted to the wavelengths a thousand times than those at which it was emitted.

We know when the black body approaches us, the Doppler shift shortens the wavelength of its light and because it to mimic a black body of higher temperature, When a black body recedes, it mimics a cooler black body. Alpher and Herman predicted that the glow from the fireball should now be at radio wavelengths and should resemble the radiation from a black body at a temperature of only 5 K- just little degree above absolute zero, unfortunately, there was no way in 1948 of observing such radiation from space. Thus the prediction does not attract much attention. However, in mid 1960s, the idea occurred independently to Princeton physicist Robert H. Dick who realized that microwave radio telescope could be built to detect the dying glow of big bang. During this period Arno Penzias and Robert Wilson of the Bell Laboratories used delicate microwave horn antenna to make careful measures of absolute intensity of radio radiation coming from certain places in the Galaxy, but they were plunged with some unexpected background noise in the system that they could not get rid off. They checked every thing and eliminated the Galaxy as source, also the sun and sky, the ground and even the equipment. Finally, they decided that the radiation they have been

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detecting were from space. Penzias mentioned it in a telephonic conversation with another radio astronomer B. Burke, who was aware of Princeton work. Burke got Penzias in touch with Dick and it was soon realized that the glow from primeval fireball has been observed. Since then the radiations has been very thoroughly checked throughout the entire radio spectrum. The observed microwave background radiation closely matches that expected from blackbody with a temperature of 2.7 K.

Penzias and Wilson received the Noble prize for their work in 1978, and perhaps almost equally fitted, just before his death in 1966. Lemaitre learned about the discovery of his “Vanished Brilliance”

9.7 Information from Cosmic Microwave Radiation

Faint glow of radio radiation now called cosmic background radiation (CBR). It has now been observed at many wavelengths and all observations are compatible with CBR being red shifted radiation emitted by hot gas. It indicated that the universe has been evolved from a hot uniform state. At a given wavelength CBR is extremely isotropic on a small scale, recent Soviet observations claim that CBR is isotropic on a small scale to better than a few parts in 105. The uniformity of the radiation reveals that at an age of less than a million years the universe had to be present to allow matter to gravitationally clump up to form stars and galaxies. The isotropy of the CBR put interesting constraints on the theories of star and galaxy formation.

Estimated distribution of dark matter and dark energy in the universe, the existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of cosmic microwave background radiation (CBR) anisotropies, most recently by the WMAP satellite; indicate that the universe is very close to flat. For the shape of the universe to be flat, the mass/energy density of the universe must be equal to a certain critical density. The total amount of matter in the universe (including baryons and dark matter), as measured by the CBR, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%. The most recent WMAP observations are consistent

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with a universe made up of 74% dark energy, 22% dark matter, and 4% ordinary matter.

High-precision measurements of the expansion of the universe are required to understand how the expansion rate changes over time. In general relativity, the evolution of the expansion rate is parameterized by the cosmological equation of state. Measuring the equation of state of dark energy is one of the biggest efforts in observational cosmology today.

Adding the cosmological constant to cosmology's standard FLRW metric leads to the Lambda-CDM model, which has been referred to as the “standard model” of cosmology because of its precise agreement with observations? Dark energy has been used as a crucial ingredient in a recent attempt to formulate a cyclic model for the universe.

In 1998, published observations of Type Ia supernovae ("one-A") by the High-z Supernova Search Team followed in 1999 by the Supernova Cosmology Project  suggested that the expansion of the universe is accelerating. Since then, these observations have been corroborated by several independent sources. Measurements of the background, gravitational, and the large scale structure of the cosmos as well as improved measurements of supernovae have been consistent with the Lambda-CDM model. Supernovae are useful for cosmology because they are excellent standard candles across cosmological distances. They allow the expansion history of the Universe to be measured by looking at the relationship between the distance to an object and its redshift, which gives how fast it is receding from us. The relationship is roughly linear, according to Hubble's law. It is relatively easy to measure redshift, but finding the distance to an object is more difficult. Usually, astronomers use standard candles: objects for which the intrinsic brightness, the absolute magnitude, is known. This allows the object's distance to be measured from its actually observed brightness, or apparent magnitude. Type Ia supernovae are the best-known standard candles across cosmological distances because of their extreme, and extremely consistent, brightness.

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Recent observations of supernovae are consistent with a universe made up 71.3% of dark energy and 27.4% of a combination of dark matter and baryonic matter.

9.9 Cosmological constant

The simplest explanation for dark energy is that it is simply the "cost of having space": that is, a volume of space has some intrinsic, fundamental energy. This is the cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the Greek letter Λ, the symbol used to mathematically represent this quantity. Since energy and mass are related by E = mc2, Einstein's theory of general relativity predicts that it will have a gravitational effect. It is sometimes called a vacuum energy because it is the energy density of empty vacuum. In fact, most theories of particle physics predict vacuum fluctuations that would give the vacuum this sort of energy. This is related to the Casimir Effect, in which there is a small suction into regions where virtual particles are geometrically inhibited from forming (e.g. between plates with tiny separation). The cosmological constant is estimated by cosmologists to be on the order of 10−29g/cm³, or about 10−120 in reduced Planck units. However, particle physics predicts a natural value of 1 in reduced Planck units, a large discrepancy which is still not explained.

The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate. The reason why a cosmological constant has negative pressure can be seen from classical thermodynamics; Energy must be lost from inside a container to do work on the container. A change in volume dV requires work done equal to a change of energy −p dV, where p is the pressure. But the amount of energy in a box of vacuum energy actually increases when the volume increases (dV is positive), because the energy is equal to ρV, where ρ (rho) is the energy density of the cosmological constant. Therefore, p is negative and, in fact, p = −ρ.

A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum, more than 100 orders of magnitude too large. This would need to be cancelled almost, but not exactly, by an equally

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large term of the opposite sign. Some super symmetric theories require a cosmological constant that is exactly zero, which does not help. The present scientific consensus amounts to extrapolating the empirical evidence where it is relevant to predictions, and fine-tuning theories until a more elegant solution is found. Technically, this amounts to checking theories against macroscopic observations. Unfortunately, as the known error-margin in the constant predicts the fate of the universe more than its present state, many such "deeper" questions remain unknown.

Another problem arises with inclusion of the cosmic constant in the standard model: i.e., the appearance of solutions with regions of discontinuities at low matter density. Discontinuity also affects the past sign of the pressure assigned to the cosmic constant, changing from the current negative pressure to attractive, as one looks back towards the early Universe. A systematic, model-independent evaluation of the supernovae data supporting inclusion of the cosmic constant in the standard model indicates these data suffer systematic error. The supernovae data are not overwhelming evidence for an accelerating Universe expansion which may be simply gliding. A numerical evaluation of WMAP and supernovae data for evidence that our local group exists in a local void with poor matter density compared to other locations, uncovered possible conflict in the analysis used to support the cosmic constant. These findings should be considered shortcomings of the standard model, but only when a term for vacuum energy is included.

In spite of its problems, the cosmological constant is in many respects the most economical solution to the problem of cosmic acceleration. One number successfully explains a multitude of observations. Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant as an essential feature.

9.10 Quintessence

In quintessence models of dark energy, the observed acceleration of the scale factor is caused by the potential energy of a dynamical field, referred to as quintessence field. Quintessence differs from the cosmological constant in that it can vary in space and time. In order

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for it not to clump and form structure like matter, the field must be very light so that it has a large Compton wavelength.

No evidence of quintessence is yet available, but it has not been ruled out either. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some scientists think that the best evidence for quintessence would come from violations of Einstein's equivalence principle and variation of the fundamental constants in space or time. Scalar fields are predicted by the standard model and string theory, but an analogous problem to the cosmological constant problem occurs: renormalization theory predicts that scalar fields should acquire large masses.

The cosmic coincidence problem asks why the cosmic acceleration began when it did. If cosmic acceleration began earlier in the universe, structures such as galaxies would never have had time to form and life, at least as we know it would never have had a chance to exist. Proponents of the entropic principle view this as support for their arguments. However, many models of quintessence have a so-called tracker behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter-radiation equality, which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy.

In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w=1) from above to below. A No-Go theorem has been proved that to give this scenario at least two degrees of freedom are required for dark energy models. This scenario is so-called Quintom scenario.

Some special cases of quintessence are phantom energy, in which the energy density of quintessence actually increases with time, and k-essence (short for kinetic quintessence) which has a non-standard form of kinetic energy. They can have unusual properties: phantom energy, for example, can cause a Big Rip.

9.11 Alternative ideas

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Some theorists think that dark energy and cosmic acceleration are a failure of general relativity on very large scales, larger than superclusters. It is a tremendous extrapolation to think that our law of gravity, which works so well in the solar system, should work without correction on the scale of the universe. Most attempts at modifying general relativity, however, have turned out to be either equivalent to theories of quintessence, or inconsistent with observations. It is of interest to note that if the equation for gravity were to approach r instead of r2 at large, intergalactic distances, then the acceleration of the expansion of the universe becomes a mathematical artifact negating the need for the existence of Dark Energy.

9.12 Implications for the fate of the universe

Cosmologists estimate that the acceleration began roughly 5 billion years ago. Before that, it is thought that the expansion was decelerating, due to the attractive influence of dark matter and baryons. The density of dark matter in an expanding universe decreases more quickly than dark energy, and eventually the dark energy dominate. Specifically, when the volume of the universe doubles, the density of dark matter is halved but the density of dark energy is nearly unchanged (it is exactly constant in the case of a cosmological constant).

If the acceleration continues indefinitely, the ultimate result will be that galaxies outside the local supercluster will move beyond the cosmic horizon: they will no longer be visible, because their line-of-sight velocity becomes greater than the speed of light. This is not a violation of special relativity, and the effect cannot be used to send a signal between them. (Actually there is no way to even define "relative speed" in a curved space time. Relative speed and velocity can only be meaningfully defined in flat space time or in sufficiently small (infinitesimal) regions of curved space time). Rather, it prevents any communication between them as the objects pass out of contact. The Earth, the Milky Way and the Virgo supercluster, however, would remain virtually undisturbed while the rest of the universe recedes. In this scenario, the local supercluster would ultimately suffer heat death, just as was thought for the flat, matter-dominated universe, before measurements of cosmic acceleration.

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There are some very speculative ideas about the future of the universe. One suggests that phantom energy causes divergent expansion, which would imply that the effective force of dark energy continues growing until it dominates all other forces in the universe. Under this scenario, dark energy would ultimately tear apart all gravitationally bound structures, including galaxies and solar systems, and eventually overcome the electrical and nuclear forces to tear apart atoms themselves, ending the universe in a "Big Rip". On the other hand, dark energy might dissipate with time, or even become attractive. Such uncertainties leave open the possibility that gravity might yet rule the day and lead to a universe that contracts in on itself in a "Big Crunch". Some scenarios, such as the cyclic model suggest this could be the case. While these ideas are not supported by observations, they are not ruled out. Measurements of acceleration are crucial to determining the ultimate fate of the universe in big bang theory.

9.13 History

The cosmological constant was first proposed by Einstein as a mechanism to obtain a stable solution of the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity. Not only was the mechanism an inelegant example of fine-tuning, it was soon realized that Einstein's static universe would actually be unstable because local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout the universe. More importantly, observations made by Edwin Hubble showed that the universe appears to be expanding and not static at all. Einstein famously referred to his failure to predict the idea of a dynamic universe, in contrast to a static universe, as his greatest blunder. Following this realization, the cosmological constant was largely ignored as a historical curiosity.

Alan Guth proposed in the 1970s that a negative pressure field, similar in concept to dark energy, could drive cosmic inflation in the

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very early universe. Inflation postulates that some repulsive force, qualitatively similar to dark energy, resulted in an enormous and exponential expansion of the universe slightly after the Big Bang. Such expansion is an essential feature of most current models of the Big Bang. However, inflation must have occurred at a much higher energy density than the dark energy we observe today and is thought to have completely ended when the universe was just a fraction of a second old. It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was thought to be irrelevant to the current universe.

Summery

There is High degree of homogeneity in the universe. The future of the universe depends on mean density of the

matter in the space.

Dark energy is the hypothetical form of energy that permeates all of the space and tends to increase the rate of expansion of universe.

Two forms of dark energy are Cosmological constant and quintessence.

Strong constant negative pressure in the entire universe causes acceleration in universe expansion if the universe is already expanding or a deceleration in universe contraction if the universe is already contracting.

The Hubble constant is now believed to lie in the range 50 to 100 Km/s per million parsecs.

The most recent WMAP observations are consistent with a universe made up of 74% dark energy, 22% dark matter, and 4% ordinary matter.

The cosmological constant has negative pressure equal to its energy density and so causes the expansion of the universe to accelerate.

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Quintessence differs from the cosmological constant in that it can vary in space and time.

Measurements of acceleration are crucial to determining the ultimate fate of the universe in big bang theory.

ExercisesFill in the blanks

1. Remote objects in the space are _____________ documents in the universe.

2. Future of the universe depends on ____________ of the matter in the space.

3. Amount of deuterium formed depends critically on the ____________ of the fireball.

4. The ratio of hydrogen to helium is _____ by mass as observed in the space.

5. Universe is made up of 74% dark energy, 22% of dark matter and 4% of __________ matter.

6. Cosmological constant is essential feature of ___________ model.

7. Big Bang model was first proposed by _________________.8. Radiations from Big Bang indicate high degree of

___________ in universe.9. Two forms of dark energies are ___________ and _________.10 Stars and galaxies began to form about ____years after

Big Bang.

Short questions with answerQ1. Does the hierarchy in the order of the cluster of galaxies go on

for ever?Ans. The available evidence suggests that it does not because. First,

if it did, it would never be possible to define a region of space beyond which the universe is homogeneous because large hierarchal structures would always exist. This would violet the cosmological principle as against the observations. Further the superclusters appear to expanding and the meager evidence suggests that most are not gravitationally bound. If superclusters are not gravitationally bound, the next order cluster should expand more rapidly and the order beyond them

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more so yet. It is hard to see how this hierarchal structure be maintained.

Q2. What is the evidence that suggest that the universe is homogeneous?

Ans. The uniformity of the faint background of radio radiations that we interpret as dying glow of big bang that started the expansion of the universe in different directions is impressive and argues for higher high degree of homogeneity in the universe at large.

Q3. On what does the future of the universe depends?Ans. The future of the universe depends critically on mean density of

the matter in space. Since it would add to the mass and hence the gravitation of the universe, but not to the light.

Q4. What is the dark Energy?Ans. Dark energy is a hypothetical form of energy that permeates all

of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be expanding at an accelerating. In the standard model of cosmology, dark energy currently accounts for 74% of the total mass-energy of the universe.

Q5. What are the forms of Dark Energy?Ans. Two proposed forms for dark energy are the cosmological

constant, a constant energy density filling space homogeneously, and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space.

Q6. Define cosmological constant?Ans. The cosmological constant was first proposed by Einstein as a

mechanism to obtain a stable solution of the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity. The cosmological constant, sometimes called Lambda (hence Lambda-CDM model) after the Greek letter Λ, is the simplest explanation for dark energy, it is simply the "cost of having space".

Q7. What was the condition of the universe when it was 100s old?Ans. By the time the universe was 100 s old, the temperature has

dropped to 109 K and the particles began to combine to form

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heavier nuclei, this neucleosynthesis continued for next few minutes during which about 25 percent of the mass of the material formed into helium.

Q8. What do you understand by the uniformity of cosmic background radiation?

Ans. The uniformity of the radiation reveals that at an age of less than a million years the universe had to be present to allow matter to gravitationally clump up to form stars and galaxies.

Q9. Why supernova is useful in cosmological models?Ans. Supernovae are useful for cosmology because they are

excellent standard candles across cosmological distances. They allow the expansion history of the Universe to be measured by looking at the relationship between the distance to an object and its redshift, which gives how fast it is receding from us.

Study QuestionsQ1. Define Dark Energy?Q2. What is Dark Matter? How does it affect the universe?Q3. What are the effects of negative pressure?Q4. When does universe became transparent?Q5. Write a short note on Cosmic Microwave Background

Radiation?Q6. What is Quintessence? How it differ from cosmological

constant?Q7. What is divergent expansion of universe? How it is

responsible for ‘Big Rip’?Q8. Write a note on Cosmological constant.Q9. Explain Hubble expansion model.Q10.Discuss the standard model of Big Bang.Q11.Write a note on cosmic background radiation.Q12. What is the significance of dark energy in the fate of

the universe?

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Silently, one by one,in the infinite meadows of the heaven,

blossumed the lovely stars,the forget-me-nots of the angels.

— Henry Wadsworth Longfellow, Evangeline, 1847

Appendix A

The Constellations

A complete table with information about all the 88 Constellations as defined by the I.A.U. (International Astronomical Union).

No.

Abbrev. Constellation Genitive

English Name

Area

Hem. Alpha Star

1 And Andromeda Andromedae Andromeda 722 NH Alpheratz

2 Ant Antlia Antliae Air Pump 239 SH  

3 Aps Apus ApodisBird of Paradise 206 SH  

4 Aqr Aquarius Aquarii Water Carrier 980 SH Sadalmelik

5 Aql Aquila Aquilae Eagle 652NH-SH Altair

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6 Ara Ara Arae Altar 237 SH  

7 Ari Aries Arietis Ram 441 NH Hamal

8 Aur Auriga Aurigae Charioteer 657 NH Capella

9 Boo Bootes Bootis Herdsman 907 NH Arcturus

10 Cae Caelum Caeli Chisel 125 SH  

11 Cam Camelopardalis

Camelopardalis Giraffe 757 NH  

12 Cnc Cancer Cancri Crab 506 NH Acubens

13 CVn Canes Venatici

Canun Venaticorum

Hunting Dogs 465 NH Cor Caroli

14 CMa Canis Major Canis Majoris Big Dog 380 SH Sirius

15 CMi Canis Minor Canis Minoris Little Dog 183 NH Procyon

16 Cap Capricornus Capricorni

Goat ( Capricorn ) 414 SH Algedi

17 Car Carina Carinae Keel 494 SH Canopus

18 Cas Cassiopeia Cassiopeiae Cassiopeia 598 NH Schedar

19 Cen Centaurus Centauri Centaur 106

0 SH Rigil Kentaurus

20 Cep Cepheus Cephei Cepheus 588 SH Alderamin

21 Cet Cetus Ceti Whale 123

1 SH Menkar

22 Cha Chamaleon Chamaleontis

Chameleon 132 SH  

23 Cir Circinus Circini Compasses 93 SH  

24 Col Columba Columbae Dove 270 SH Phact

25 Com Coma Berenices

Comae Berenices

Berenice's Hair 386 NH Diadem

26 CrA Corona Australis

Coronae Australis

Southern Crown 128 SH  

27 CrB Corona Borealis

Coronae Borealis

Northern Crown 179 NH Alphecca

28 Crv Corvus Corvi Crow 184 SH Alchiba

29 Crt Crater Crateris Cup 282 SH Alkes

30 Cru Crux Crucis Southern 68 SH Acrux

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Cross

31 Cyg Cygnus Cygni Swan 804 NH Deneb

32 Del Delphinus Delphini Dolphin 189 NH Sualocin

33 Dor Dorado Doradus Goldfish 179 SH  

34 Dra Draco Draconis Dragon 108

3 NH Thuban

35 Equ Equuleus Equulei Little Horse 72 NH Kitalpha

36 Eri Eridanus Eridani River 113

8 SH Achernar

37 For Fornax Fornacis Furnace 398 SH  

38 Gem Gemini Geminorum Twins 514 NH Castor

39 Gru Grus Gruis Crane 366 SH Al Na'ir

40 Her Hercules Herculis Hercules 122

5 NH Rasalgethi

41 Hor Horologium Horologii Clock 249 SH  

42 Hya Hydra Hydrae

Hydra ( Sea Serpent )

1303 SH Alphard

43 Hyi Hydrus Hydri

Water Serpen ( male ) 243 SH  

44 Ind Indus Indi Indian 294 SH  

45 Lac Lacerta Lacertae Lizard 201 NH  

46 Leo Leo Leonis Lion 947 NH Regulus

47 LMi Leo Minor Leonis Minoris

Smaller Lion 232 NH  

48 Lep Lepus Leporis Hare 290 SH Arneb

49 Lib Libra Librae Balance 538 SH Zubenelgenubi

50 Lup Lupus Lupi Wolf 334 SH Men

51 Lyn Lynx Lyncis Lynx 545 NH  

52 Lyr Lyra Lyrae Lyre 286 NH Vega

53 Men Mensa Mensae Table 153 SH  

54 Mic Microscopium Microscopii

Microscope 210 SH  

55 Mon Monoceros Monocerotis Unicorn 482 SH  

56 Mus Musca Muscae Fly 138 SH  

57 Nor Norma Normae Square 165 SH  

58 Oct Octans Octantis Octant 291 SH  

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59 Oph Ophiucus Ophiuchi Serpent Holder 948

NH-SH Rasalhague

60 Ori Orion Orionis Orion 594NH-SH Betelgeuse

61 Pav Pavo Pavonis Peacock 378 SH Peacock

62 Peg Pegasus Pegasi Winged Horse

1121 NH Markab

63 Per Perseus Persei Perseus 615 NH Mirfak

64 Phe Phoenix Phoenicis Phoenix 469 SH Ankaa

65 Pic Pictor Pictoris Easel 247 SH  

66 Psc Pisces Piscium Fishes 889 NH Alrischa

67 PsA Pisces Austrinus

Pisces Austrini

Southern Fish 245 SH Fomalhaut

68 Pup Puppis Puppis Stern 673 SH  

69 Pyx Pyxis Pyxidis Compass 221 SH  

70 Ret Reticulum Reticuli Reticle 114 SH  

71 Sge Sagitta Sagittae Arrow 80 NH  

72 Sgr Sagittarius Sagittarii Archer 867 SH Rukbat

73 Sco Scorpius Scorpii Scorpion 497 SH Antares

74 Scl Sculptor Sculptoris Sculptor 475 SH  

75 Sct Scutum Scuti Shield 109 SH  

76 Ser Serpens Serpentis Serpent 637NH-SH Unuck al Hai

77 Sex Sextans Sextantis Sextant 314 SH  

78 Tau Taurus Tauri Bull 797 NH Aldebaran

79 Tel Telescopium Telescopii Telescope 252 SH  

80 Tri Triangulum Trianguli Triangle 132 NH Ras al Mothallah

81 TrA Triangulum Australe

Trianguli Australis

Southern Triangle 110 SH Atria

82 Tuc Tucana Tucanae Toucan 295 SH  

83 UMa Ursa Major Ursae Majoris

Great Bear

1280 NH Dubhe

84 UMi Ursa Minor Ursae Minoris

Little Bear 256 NH Polaris

85 Vel Vela Velorum Sails 500 SH  

86 Vir Virgo Virginis Virgin 129

4NH-SH Spica

87 Vol Volans Volantis Flying 141 SH  

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Fish

88 Vul Vulpecula Vulpeculae Fox 268 NH  

ABBREV: IAU abbreviationCONSTELLATION: Latin nameGENITIVE: Latin genitive (Possessive) ENGLISH NAME: English translationAREA: constellation size or area, in square degreesHEM: position in the celestial sphere:          NH - northern celestial hemisphere - declination between

0° and +90°          SH - southern celestial hemisphere - declination between

0° and - 90°ALPHA STAR: proper name of the alpha star.

Appendix BSome Constants

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Quantity Symbol ValueMathematical constants

Pi Π 3.1415926536Radian Rad. 57º.12957795

3437’.174677206264’’.80

Number of square degrees on a sphere

41252.96124

Physical ConstantsVelocity of light C 2.99792458 x 1010 cm/sConstant of gravitation G 6.672 x 10-8 dynes.cm2/g2

Plank’s constant h 6,626 x 10-27ergs.sBoltzmann’s constant K 1.381 x 10-16 erg/degMass of hydrogen atom m h 1.673 x 10-24 gMass of electron m e 9.1095 x 10-28 gCharge on electron e 4.803 x 10-10 electrostatic

unitsStefan-Boltzmann constant σ 5.670 x 10 -5 erg/ cm2 .deg4 .sRydberg’s constant R∞ 6.6x10-12

1 electron volt eV 1.60217653x10-19 JAstronomical ConstantsAstronomical unit A.U. 1.496 x 1011 meters

=149,597,870.691 kmParsec pc 3.0857x1016 m

= 3.08567802× 1013 km = 206,265 A.U.

Light year ly 9.4605x1015 m= 9.460536207× 1012 km = 63,240 A.U.

Tropical year 365.242199 ephemeris daysSidereal year 365.256366 ephemeris daysMass of earth 5.977 × 1027 gMass of sun 1.9818 × 1038 gSolar Radius 6.9599x108 mSolar Luminosity 3.90x1026 W

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Appendix cAstronomical coordinate system

One of the basic needs of astronomy, as well as other physical sciences, is to give reasonable descriptions for the positions of objects relative to each other. Scientifically, this is done in mathematical language, by properly assigning numbers to each position in space; these numbers are called coordinates and the system defined by this procedure a coordinate system.

The coordinate systems considered here are all based at one reference point in space with respect to which the positions are measured, the origin of the reference frame (typically, the location of the observer, or the center of Earth, the Sun, or the Milky Way Galaxy). Any location in space is then described by the "radius vector" or "arrow" between the origin and the location, namely by the distance (length of the vector) and its direction. The direction is given by the straight half line from the origin through the location (to infinity). In the spherical coordinate systems used here, the direction is fixed by two angles, which are given as follows:

A reference plane containing the origin is fixed, or equivalently the axis through the origin and perpendicular to it (typically, an "equatorial" plane and a "polar" axis); elementarily, each of these uniquely determines the other. One can assign an orientation to the polar axis from "negative" to "positive", or "south" to "north", and simultaneously to the equatorial plane by assigning a positive sense of rotation to the equatorial plane; these orientations are, by convention, usually combined by the right hand rule: If the thumb of the right hand point to the positive (north) polar axis, the fingers show in the positive direction of rotation (and vice versa, so that a physical rotation defines a north direction).

The reference plane or the reference axis define the set of planes which contain the origin and are perpendicular to the "equatorial" reference plane (or equivalently, contain the "polar" reference axis); each direction in space then lies precisely in one of these "meridional" planes (or half planes, if the reference axis is taken to divide each plane into halfs), with the exception of the (positive and negative) polar axis which lies in all of them by definition.

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The first angle used to characterize a direction, typically the "latitude", is taken between the direction and the reference plane, within the "meridional" plane. For the second angle, it is required to select and fix one of the "meridional" half planes as zero, from which the angle (of "longitude") is measured to the "meridional" half plane containing our direction.

It should be noted that this selection of angles to characterize a direction in a given reference frame is chosen by convention, which is especially common in astronomy and geography, and which is used in the following here, as well as in most astronomical databases. Other, equivalent, conventions are possible, e.g. physicists often use instead of the "latitude" angle to the reference plane, the angle between the direction and the "positive" or "north" polar axis (called "co-latitude"; co-latitde = 90 deg - latitude). It depends on taste at last what the reader likes to use, but here we will stay as close to standard astronomical convention as possible. In order to minimize the requirement of case-to-case enumeration of conventions, we also recommend the reader to do the same. The different coordinate systems used are as follows:

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This conveniently divides the sky into the upper hemisphere that you can see, and the lower hemisphere that you cannot (because the Earth is in the way). The pole of the upper hemisphere is called the zenith. The pole of the lower hemisphere is called the nadir.

The horizontal coordinates are:

Altitude (Alt), sometimes referred to as elevation, that is the angle between the object and the observer's local horizon.

Azimuth (Az), that is the angle of the object around the horizon, usually measured from the north point towards the east. In former times, it was common to refer to azimuth from the south, as it was then zero at the same time the hour angle of a star was zero. This assumes, however, that the star (upper) culminates in the south, which is only true for most stars in the Northern Hemisphere. The horizontal coordinate system is sometimes also called the az/el or Alt/Az coordinate system.

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Figure A 1: HORIZONTAL COORDINATES. Azimuth, from the North point (red) -also from the South point toward the West (blue). Altitude, green.

One can determine whether altitude is increasing or decreasing by instead considering the azimuth of the celestial object:

if the azimuth is between 0° and 180° (north–east–south), it is rising.

if the azimuth is between 180° and 360° (south–west–north), it is setting.

Equatorial coordinate system is a widely-used method of mapping celestial objects. It functions by projecting the Earth's geographic poles and equator onto the celestial sphere. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles, respectively.

Figure A 1: Equatorial Coordinate system

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The equatorial coordinate system allows all earthbound observers to describe the apparent location in the sky of sufficiently distant objects using the same pair of numbers: the right ascension and declination. For example, a given star has roughly constant equatorial coordinates. In contrast, in the horizontal coordinate system, a star's position in the sky is different based on the geographical latitude and longitude of the observer, and is constantly changing based on the time of day.

Ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. The ecliptic is the path that the sun appears to follow across the sky over the course of a year. It is also the projection of the Earth's orbital plane onto the celestial sphere. The latitudinal angle is called the ecliptic latitude or celestial latitude (denoted β), measured positive towards the north. The longitudinal angle is called the ecliptic longitude or celestial longitude (denoted λ), measured eastwards from 0° to 360°. Like right ascension in the equatorial coordinate system, the origin for ecliptic longitude is the vernal equinox. This choice makes the coordinates of the fixed stars subject to shifts due to the precession, so that always a reference epoch should be specified. Usually epoch J2000.0 is taken, but the instantaneous equinox of the day (called the epoch of date) is possible too.

Figure A 1: Ecliptic Coordinate Sysyem

Galactic coordinate system is a celestial coordinate system which is centered on the Sun and is aligned with the apparent center of the Milky Way galaxy. The "equator" is aligned to the galactic plane.

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Similar to geographic coordinates, positions in the galactic coordinate system have latitudes and longitudes.

Figure A 1: Galactic Coorsinate system. An artist's depiction of the Milky Way galaxy, showing the galactic longitude relative to the sun.

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Appendix D

GlossaryAberration (of starlight). Apparent displacement in the direction of the star due to earth’s orbital motion.Absolute magnitude. Apparent magnitude a star would have at a distance of 10 pcAbsolute zero. A temperature of -273 C (or 0 K) where all molecular motion stopsAccelerate. To change velocity ; either to speed up , slow down or change directionAcceleration of gravity Numerical value of the acceleration produced by the gravitational attraction on

an object at the surface of the planet or a starAccretion Gradual accumulation of mass, as by a planet forming by the building up of

colliding particles in the solar systemActive galactic nucleus A violent event in the nucleus of a galaxy; for example a Seyfert galaxy or a

quasar Active sun The sun in the times of unusual solar activity- spots, flares, add associated

phenomenaAltitude Angular distance above or below the horizon, measured along the vertical

circle, to the central objectAngstrom (ºA) Unit of length equal to 10-8 cmAngular diameter Angle subtended by the diameter of an objectAngular momentum A measure of the momentum associated with the motion about an axis or fixed

point.Antimatter Matter consisting of antiparticles; antiprotons (protons with negative rather

then positive charge), positrons (positively charged electrons), and antineutrons.

Apparent magnitude A measure of the observed light flux received from the star or object at the earth.

Artificial satellite A manmade object put into closed orbit about the earth.Associations A loose cluster of stars whose spectral types, motions, or position in the sky

indicate that they have probably the common origin Astrology The pseudoscience3that treat with supposed influences of the configurations

and locations in the sky on the sun, moon and planets on human destiny; a primitive religion having its origin in ancient Babylonia.

Astrometric binary A binary star in which one component is not observed, but its presence is detected from the orbital motion of the visible component

Astronomical unit (AU) Originally meant to be the semi major axis of the orbit of earth; now defined as the semi major axis of the orbit of a hypothetical body with the mass and period that Gauss assumed for the earth. The semi major axis of the orbot of the earth is 1.000000230 AU

Astronomy The branch of science that treats of the physics and morphology of that part of the universe that lies beyond the earths atmosphere

Astrophysics A Part of astronomy that deals principally with the physics of the stars, stellar systems, and interstellar material. Astrophysics also deals with the structure and atmosphere of the sun

Barred spiral galaxy Spiral galaxy in which the spiral arm begin from the end of a “bar”, running through the nucleus rather than the nucleus itself

Barycenter A center of mass of two mutually revolving bodiesBe star A spectral type b star with emission lines in the spectrum, which are

presumed to arise from material ejected from or surroundings of star Big bang theory A theory of cosmology in which the expansion of universe is presumed to have

begun with primeval explosionBinary star A double star; two stars revolving about each otherBlack dwarf A presumed final state of evolution for a star, in which all its energy sources

are exhausted and it no longer emits any radiation.Black hole A hypothetical body whose velocity of escape is equal to or greater than the

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velocity of light; that no radiation can escape.Bode’s law A scheme by which a sequence of numbers can be obtained that gives the

approximate distances of the planets from the sun in astronomical units.Bolometric magnitude A measure of the flux of radiation from a star or other object received just

outside the earth’s atmosphere, as it would be detected by a device sensitive to all form of electromagnetic energy.

Busrter A source of sudden bursts of X rays, believed to be neutron star accreting mass from a companion star, and suddenly igniting that material in nuclear explosions.

cD galaxy A supergiant elliptical galaxy frequently found at the Center of the cluster of galaxies.

Celestial mechanics That branch of astronomy which deals with the motions and gravitational influences of the member of the solar system

Cephide variables A star that belong to one or two classes (type I and type Ii) of yellow supergiant pulsating stars.

Ceres Largest of the dwarf planets and first to be discovered.Clouds of Magellan Two neighboring galaxies visible to naked eyes fron southern latitudesCluster of galaxies A system of galaxies containing from several to thousands of galaxies.Cluster variables (RR Lyrae variables)

A member of a certain large class of pulsating variable stars, all with period less than one day.. these stars are often present in globular star clusters

Color index Difference between the magnitude of a star or other object measured in light of two different spectral regions, e.g. photographic minus photo visual magnitudes.

Color-magnitude diagram Plot of magnitudes (apparent and absolute) of the stars in cluster against their color index.

Comet A small body of ice and dusty matter, which revolves about the sun. when the comet comes near the sun, some of its material vaporizes, forming a large coma of tenuous gas, and often a tail

Compact galaxy A galaxy of small size and high surface brightness.Constellation A configuration of stars named for a particular object, person or animal; or the

area of sky assigned to a particular configurationCorona Atmosphere of the sun.Corona of galaxy Extension of the nuclear bulge of the galaxy on the either side of the plane of

the milky way; a region containing hot gases that emit X rays.Corpuscular radiation Charged particles, mostly atomic nuclei and electrons, emitted into space by

the sun and possibly other objects.Cosmic background radiation (CBR)

The microwave radiation coming from all directions that is believed to be redshifted glow of big bang.

Cosmic rays Atomic nuclei 9mostly protons) that are observed to strike the earth’s atmosphere with exceedingly high energy.

Cosmological constant A term that arises in the development of field equations of general relativity, which represents a repulsive force in the universe. It is often assumed to be zero.

Cosmological model A specific model or theory of organization and evolution of universe.Cosmology A study of organization and evolution of universe.Crab nebula The expanding mass of gas that is the remnant of supernova of 1054.Dark nebula A cloud of interstellar dust that obscures the light of more distant stars and

appears as an opaque curtain.Deceleration parameter (qo) A quantity that characterizes the future evolution of the various models of the

universe based on general relativity. Degenerate gas A gas in which the allowable states for the electrons have been filled; it

behaves according to different laws from those that apply to “perfect’ gasesDensity The ratio of the mass of the object to its volume.Deuterium A “heavy” form of hydrogen, in which the nucleus of each atom consists of one

proton and one neutron.Differential galactic rotation The rotation of galaxy, not as solid wheel, but so that parts adjacent to each

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other do not always stay close together.Differential gravitational force The difference between respective gravitational forces exerted on two bodies

near each other by a third more distant body.Diffuse nebula A reflection of emission nebula produced by interstellar matter (not a planetary

nebula).Disk (of planet or other objects) The apparent circular shape that a planet ( or the sun , or moon or a star)

displays when seen in the sky or viewed telescopically.Disk of Galaxy The central disk or wheel of our Galaxy, superimposed on the spiral structureDiurnal Daily.Doppler shift Apparent change in wavelength of the radiation from a source due to its

relative motion in the line of sightDwarf (star) A main sequence star (as oppose to giant or supergiant).Eccentric The off-center position of the earth in the presumed circular orbits of the sun,

moon, and planets in Ptolemaic system.Eccentricity (of ellipse) Ratio of the distance between the foci to the major axis.Eclipse Cutting off of all parts of light of one body by another passing in front of it.Eclipsing binary A binary star in which the plane of revolution of two stars is nearly edge on to

our line of sight, so that the light of one of the star is periodically diminished by the other passing in front of it.

Electromagnetic force One of the four fundamental forces of the nature ; the force that acts on charges and binds the atom and molecules.

Electromagnetic radiation Radiation consisting of waves propagated through the building up and breaking down of electric and magnetic fields; these include radio, infrared, light, ultraviolet, X rays and gamma rays.

Electromagnetic spectrum The whole array or family of electromagnetic waves.Electron A negatively charged sub atomic particle that normally move about the nucleus

of an atom.Element A substance that cannot be decomposed , by chemical means , into simpler

substances.Elliptical galaxy A galaxy whose apparent photometric contours are ellipses, and which

contains no conspicuous interstellar material.Emission nebula A gaseous nebula that derives its visible light from the fluorescence of

ultraviolet light from a star in ior near the nebula.Energy Ability to do work.Equation of state An equation relating the pressure, temperature and density of a substance

(usually a gas).Equator A great circle on earth , 90º from polesEruptive variable A variable star whose changes in light are erratic or explosive.Event A point in four dimensional spacetime.Event horizon The surface through which a collapsing star is hypothesized to pass when its

velocity of escape is equal to the speed of light, that is, when star become a black hole.

Evolutionary cosmology A theory of cosmology that assumes that all parts of universe have the common age and evolved together.

Extragalactic Beyond Galaxy.Fission A breakup of heavy atomic nucleus into two or more lighter ones.Flare A sudden and temporary outburst of light from an extended region of solar

surface.Flare star A member of the class of stars that show occasional, sudden, unpredicted

increase in light.Fluorescence The absorption of light of one wavelength and reemission of it at another

wavelength; especially the conversion of ultraviolet into visible light.Flux The rate at which the energy or matter crosses a unit area of a surface.Force That which can change the momentum of a body, numerically, the rate at

which the body’s momentum changes.Fusion The building up of heavier atomic nuclei from lighter ones.

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Galactic cluster An “open”: cluster of stars located in the spiral arm s or disk of Galaxy.Galactic equator Intersection of the principal plane of Milky Way with the celestial sphereGalactic latitude Angular distance north or south of galactic equator to an object, measures

along a great circle passing through the object and the galactic poles. Galactic longitude Angular distance measured east or west along the galactic equator from the

galactic center, to the intersection of galactic equator with great circle passing through the galactic poles and an object.

Galactic poles The poles of the galactic equator; the intersection with the celestial sphere of a line through the observer that is perpendicular to the plane of galactic equator.

Galactic rotation Rotation of Galaxy.galaxy A large number of stars; a typical galaxy contains millions to hundreds of

thousands of millions of stars.Galaxy The galaxy to which the sun and our neighboring stars belong; the Milky Way

is the light from remote stars in the Galaxy.Geodesic The path of the body in spacetime.Giant (star) A star of large luminosity and radius.Globular cluster One of about 120 large star clusters that forms a system of clusters centered

on the center of our GalaxyGlobule A small, dense, dark nebula; believed to be a possible site of star formation.Gravitation The tendency of matter to attract itself.Gravitational constant G The constant of proportionality in Newton’s law of gravitation; in metric unit g

has the value 6.627x10 -8 dyne.cm2/gm2

Gravitational energy Energy that can be released by the gravitational collapse of, or partial collapse of a system.

Gravitational lens A configuration of celestial objects, one of which provides one or more images of the other by gravitationally deflecting its light.

Gravitational redshift The redshift caused by a gravitational field. The showing of clocks in gravitational field.

Gravitational waves Oscillations in spacetime propagated by the changes in the distribution of matter.

Halo (around the sun or moon) A ring of light around the sun or moon caused by the refraction by the ice crystals of cirrus clouds.

Halo (of galaxy) The outermost extent of our Galaxy or another, containing the sparse distribution of stars and globular clusters in a more or less spherical distribution.

Harmonic law Kepler’s third law of planetary motion: the cube of semimajor axis of the planetary orbits is proportional to the square of the sidereal periods of the planetary revolutions about the sun.

Hayashi line The track of evolution on the Hertzsprung-Russell diagram of a completely convective star.

Helio Prefix referring to the sun.Heliocentric Centered on the sun.Helium flash The nearly explosive ignition of helium in the triple alpha process in the dense

core of a red giant star. Helmholtz-Kelvin contraction The gradual gravitational contraction of a cloud of or a star, with the release of

the gravitational potential energy.Hertzsprung gap A v shaped gap in the upper part of Hertzsprung-Russell diagram where few

stable stars are formed.Hertzsprung-Russell (H-R)diagram A plot of absolute magnitude against temperature (or spectral class or color

index) for a group of stars.Homogenous star (or stellar model) A star (or theoretical model of a star) whose chemical composition is same

throughout its interior.Horizon (astronomical) A great circle in the celestial sphere 90º from the zenith.Horizon system A system of celestial coordinates (altitude and azimuth) based on the

astronomical horizon and north point.Horizontal branch A sequence of stars on Hertzsprung-Russell diagram of a typical globular

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cluster of approximately constant absolute magnitude (near Mo=0)Hubble constant A constant of proportionality between velocities of the remote galaxies and

their distances. The Hubble constant is thought to lie between 50 to 100 km/s per million persac.

Hubble law The law of redshiftHydrostatic equilibrium A balance between the weight of different layers , as in a star or the earth’s

atmosphere, and the pressure that support them.Inferior planets A planet whose distance from the sun is less than the earth’s.Interplanetary medium The sparse distribution of gas and solid particles in the interplanetary spaceInterstellar dust Microscopic solid grains, believed to be mostly dielectric compounds of

hydrogen and other common elements in interstellar space. Interstellar gas Sparse gas in interstellar space.Interstellar matter Interstellar gas and dust.Irregular galaxy A galaxy without rotational symmetry neither a spiral nor elliptical galaxy.Irregular variable A variable star whose light variations do not repeat with regular period.Island universe Historical synonym for galaxy.Jovian planets Any of the planets Jupiter, Saturn, Uranus and Neptune.Jupiter The fifth planet from the sun in the solar system.Kepler’s law Three laws, discovered by J. Kepler’s, that describes the motion of the planets.Kinetic theory (of gases) The science that treat the motion of the molecules that composes gases.Latitude A north-south coordinate on the surface of the earth; the angular distance

north or south of the equator measured along the meridian passing through a place.

Law A statement of order or relation between phenomena that, under given conditions, is presumed to be invariable.

Law of areas Kepler’s second law; the radius vector from the sun to any planet sweeps out equal areas in the planets orbital plane in equal interval of time.

Law of redshift The relation between radial velocity and distance of the remote galaxy; the radial velocities are proportional to distances of the galaxies.

Light Electromagnetic radiation that is visible to eye.Light curve A graph that displays the time variation in light or magnitude of a variable or

eclipsing binary star.Light year The distance light travels in vacuum in one year; 1LY = 9.46 x 1027 cm or about

6 x 1012mi.Limiting magnitude The faintest magnitude that can be observed with a given instrument or under

given conditions.Local group The cluster of galaxies to which our Galaxy belongs.Local super cluster The super cluster of galaxies to which the local group belongs.luminosity The rate of radiation of electromagnetic energy into space by a star or other

object.Luminosity class Classification of a star according to its luminosity for a given spectral class.Luminosity function The relative numbers of stars 9or other objects) of various luminosities or

absolute magnitudes.Magnetic fields The region of space near a magnetized body within which the magnetic forces

can be detected.Magnetosphere The region around the earth or a planet occupied by the magnetic fields.Main sequence A sequence of stars on Hertzsprung-Russell diagram, containing the majority

of stars, that runs diagonally from upper left to the lower right.Major planets A Jovian planet.Mars Forth planet from the sun in the solar system.Mass A measure of total amount of material in a body; defined either by internal

properties of the body or by its gravitational influence.Mass luminosity relation An empirical relation between masses and the luminosities of many

(particularly main sequence) stars.Mass radius relation (for white dwarfs)

A theoretical relation between the masses and radii of white dwarf stars.

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Mean density of matter in the universe

The average density of the universe if all its matter and energy could be smoothed out to absolute uniformity.

Mechanics A branch of physics which deals with the behavior of material bodies under the influence of , or in absence of forces.

Mercury The nearest planet to the sun in the solar system.Messier Catalogue A catalogue of non stellar objects compiled by Charles Massier. In 1787.Milky Way The band of light encircling the sky, which is due to many stars and diffused

nebulae lying near the plane of Galaxy.Mira Ceti-type variable star Any of the large class of red giant long period or irregular pulsating variable

stars, of which Mira is a prototype.N galaxy A galaxy with a stellar appearing nucleus with the reminder of galaxy

appearing as surrounding faint haze. Most or all N galaxies are probably either Seyfert galaxies or quasars.

nebula Cloud of interstellar gas or dust.Nebular hypothesis The basic idea that the sun and the planets formed from the same cloud of gas

and dust in interstellar space.Neptune Eighth planet from the sun in the solar system.Neutron Star A star of extremely high density composed almost entirely of neutronsNew General Catalogue (NGC) A catalogue of star clusters, nebulae, and galaxies compiled by J.L.E. Dreyer

in 1888.Newton’s law The laws of mechanics and gravitation formulated by Sir. Issac Newton.Nova A star that experiences a sudden outburst of radiant energy, temporarily

increasing its luminosity by hundreds to thousands of times.Nuclear bulge Central part of our Galaxy.Nucleosynthesis The building up of heavy elements from lighter ones.O-association A stellar association in which the stars are predominantly of types O and B.Open cluster A comparatively loose or “open” cluster of stars, containing from a few dozen

to few thousand members, located in the spiral arm of the disk of the Galaxy; galactic cluster.

Optical binary Two stars at different distances nearly lined up in projection so that they appear close together, but which are not dynamically associated

Orbit The path of the body that is in revolution about another body or point.parallax Apparent displacement of the object due to the motion of the observer.Parsec The distance of an object that would have a stellar parallax of one second of

arc; 1 parsec = 3.26 light year.Perfect cosmological principle Assumption that on the large scale, universe appears same from every place

and at all the time.Perfect gas law Certain laws that describes the behavior of the ideal gas; Charle’s law, Boyle’s

law and the equation of state for the perfect gas.Period density relation Proportionality between the period and the inverse square root of the mean

density for a pulsating star.Period luminosity relation An empirical relation between the period and luminosities of Cepheid variable

star.Photo visual magnitude A magnitude corresponding to the spectral region to which the human eye is

most sensitive, but measured by photographic methods with suitable green-and yellow- sensitive emulsion and filter.

Planet Any of the eight solid bodies revolving about the sun.Planetary nebula A shell of gas ejected from, and enlarging about , a certain kind of extremely

hot star.Plank’s constant A constant of proportionality relating energy of photon and its frequency.Population I and II Two classes of stars (and system of stars), classified according to their

spectral characteristics, chemical compositions, radial velocities, ages, and location in the Galaxy.

Primeval atom A single mass whose explosion (in some cosmological theories) has been postulated to have resulted in all the matter now present in the universe.

Primeval fireball Extremely hot opaque gas that is presumed to have comprised the entire mass

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of the universe at the time of or immediately following the “big bang”; the exploding primeval atom.

Proton sphere A surface surrounding the black hole Pulsar A variable radio source of a small angular size that emits radio pulses in very

regular periods that range from 0.03 to 3 seconds.Pulsating variable A variable star that pulsates in size and luminosity.Quantum mechanics The branch of physics that deals with the structure of the atoms and their

interactions with each other and with radiation.quasar A stellar appearing object of very high redshift, presumed to be extragalactic

and highly luminous an active galactic nucleus. Radio astronomy The technique of making astronomical observations in radio wavelengths.Radio galaxy A galaxy that emits greater amount of radio radiation than average Redgiant A large cool star of high luminosity; a star occupying the upper right portion of

Hertzsprung-Russell diagramRedshift A shift to the longer wavelength of light from remote galaxies; presumed to be

produced by Doppler shift.Reflection nebula A relatively dense dust cloud in interstellar space that is illuminated by

starlight.RR Lyrae variable One of the class of giant pulsating stars with period less than one day; a

cluster variable.Satellites A body that revolves about the large one.Saturn Sixth planet from the sun in the solar system.Schwarzschild radius See event horizonScience The attempt to find the order in the nature or to find laws that describe the

natural phenomena.Seyfery galaxy A galaxy belonging to a class of those with active galactic nuclei; one whose

nucleus shows bright emission lines; one of the classes of galaxies first described by c. Seyfert.

Solar activity Phenomena of solar atmosphere; sunspots, plages’ and related phenomena.Solar constant Mean amount of solar radiation received per unit time, by a unit area, just

outside the earths atmosphere and perpendicular to the direction of the sun; the numerical value is 1.37x 108ergs/cm2.s

Solar nebula The cloud of gas and dust from which solar system is presumed to be formed.Solar system The system of the sun and the planets, their satellites, the minor planets,

comets, meteoroids and other objects revolving around the sun.Solar wind A radial flow of corpuscular radiation leaving the sun.Spacetime A system of one time and three spatial coordinates, with respect to which the

time and place of the event can be specified.Specific gravity The ratio of the density of the body or substance to that of water.Spectral class A classification of stars according to characteristics of its spectrum.Spectral sequence A sequence of the spectral classes of the stars arranged in order of decreasing

temperatures of stars of those classes.Spectroscopic binary A binary star in which the components are not resolved optically, but whose

binary nature is indicated by periodic variation in radial velocity, indicating orbital motion.

Spectrum binary A binary star whose binary nature is revealed by spectral characteristics that can only result from the composite of the spectra of two different stars.

Spiral arms Arms of interstellar material and young stars that winds out in the plane from the central nucleus of a spiral galaxy.

Spiral galaxy A flattened, rotating galaxy with pin-wheel like arms of interstellar material and young stars winding out from its nucleus.

star A self luminous sphere of gas.Star cluster An assembly of stars held together by their mutual gravitation.Stellar evolution The change that takes place in the size, structures and so on , of star as they

ageStellar model The result of theoretical calculations of the run of physical conditions in stellar

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interior.sub dwarf A star of luminosity lower than that of main sequence star of same spectral

type.Sub giant A star of luminosity intermediate between those of main sequence star and

normal giants of same spectral type.sun The star about which earth and other planets.Super cluster A large region of space (50 to 100 million parsecs across) where matter is

concentrated into galaxies, group of galaxies and cluster of galaxies, a cluster of cluster of galaxies.

Supergiant A star of very high luminosity.Superior planet A planet more distant from the sun than the earth.supernova A stellar outburst or explosion to which a star suddenly increases its luminosity

by from hundreds of thousands to hundreds of millions of time.Surface gravity. The weight of the unit mass on the surface of the body.T association A stellar association containing T-Tauri stars.T Tauri star Variable star associated with interstellar matter that shows rapid and erratic

change in light.Terrestrial planets Any of the planets Mercury, Venus, earth and mars, and some times Pluto.Thermal equilibrium A balance between input and outflow of heat in a systemTriple alpha process A series of two nuclear reactions by which three helium nuclei are built up into

one carbon nucleus.Uranus Seventh planet from the sun in the solar system.Variable stars A star that varies in luminosity.Velocity of escape The speed with which an object must move in order to enter a parabolic orbit

about another body (such as earth) and hence move permanently away from the vicinity of that body.

Venus The second planet from the sun in the solar system.Visual binary star A binary star in which two components are telescopically resolved.Voyagers A series of space crafts that were launched by US in 1977 to explore Jupiter

and more distant planets.Wavelength The spacing of Crests and troughs in a wave train.Weight A measure of force due to gravitational attraction.White dwarf A star that has exhausted most or all of its nuclear fuel and has collapsed to a

very small size; believed to be near its final stage of evolution.Wolf-Rayet star One of the classes of the very hot stars that eject shells of gas at very high

velocity.X-ray burstersX-ray stars Stars other than sun) that emit observable amount of radiation at x- ray

frequency.Zero age main sequence Main sequence for a system of stars that have completed their contraction

from interstellar matter , are now deriving all its energy from nuclear reactions, but whose chemical composition has not yet been altered by nuclear reactions.

Zodiac A belt around the sky 18º wide centered on the ecliptic.

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Appendix E

Model Test Paper-1Note: Attempt all Questions. Total Marks: 100

Section AAttempt all parts of this question. All parts of the question carry equal marks.1. This Question contains 10 objective types/fill in the blank type /

true-false type questions (2X10=20)1. ______ cannot be defined via other quantities because nothing

more fundamental is known at the present.2. The star derives their energy by ______________ conversion.3. The heliosphere partially shields the _____________, and

planetary magnetic fields.4. Kepler believed in underlying the harmony in the nature, and he

constantly searched for ___________ relations in the celestial realm.

5. The three ways in which teat can be transported; by ________, by __________ and by ______________.

6. ___________ measurements demonstrated the vast separation of the stars in the heavens.

7. To be truly representative of stellar population a ____________should be plotted for all stars within certain distance.

8. No nonrotating white dwarf can be ___________ than the Chandrasekhar limit.

9. Galaxies differ a great deal among themselves but majority fall into two general classes____________ and ____________.

10. Universe is made up of 74% dark energy, 22% of dark matter and 4% of __________ matter.

Section B2. Attempt any three parts of the following: (3x10=30)

a) What do you understand by space science? What was the golden period of space science?

b) What is a solar system? When it is thought to be created?

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c) Describe the main characteristics of population I and II stars?d) What is Kepler’s first law? What correction did the Newton

introduced?e) What is Eddington Luminosity?

Section CAttempt all questions. All questions carry equal marks (5x10=50)3. Attempt any two parts of the following

a) What are metals in astronomy? What is the effect of metallicity on stellar evolution?

b) How we can differentiate star clusters? What are its different types?

c) What is a nebula? How do you differentiate from the galaxy?

4. Attempt any two of the following: (2X5=10)Write the note on:a) Schwarzschild radiusb) Globular Clustersc) Open Clustersd) Associations

5. Attempt any one of the following: (1X10)a) A cow attempted to jump over the moon but landed into the

orbit around the moon. Describe how the cow could be used to determine the mass of the moon?

b) What is the significance of dark energy in the fate of the universe?

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Model Test Paper-2Note: Attempt all Questions. Total Marks: 100

Section AAttempt all parts of this question. All parts of the question carry equal marks.1. This Question contains 10 objective types/fill in the blank type /

true-false type questions (2X10=20)1. There are _________ overall categories in space science

that can generally be described on their own.2. The _________ of Planets and _______ of dwarf planets are

orbited by their moons.3. Most of the material of the solar system that is not a part of

the sun itself is concentrated in the __________.4. Each planet moves about the sun in a orbit that is an ellipse,

with the sun at one focus of the __________.5. Using the stellar spectrum, astronomers can also determine

the _____________ temperature, surface gravity, metallicity and rotational velocity of a star.

6. A substantial number of stars lie above the main sequence of the H-R diagram in the upper right (cool, highly luminous), these are called ___________.

7. The structure of the neutron star is analogous to white dwarf except that neutron stars are much _____________.

8. Typical galaxies range from _________ with as few as ten million (107) stars up to __________ with one trillion (1012) stars, all orbiting the galaxy's center of mass.

9. Radiations from Big Bang indicate high degree of ___________ in universe.

10. Theories of formation of galaxies could be divided into two categories namely ______________ and _____________.

Section B2. Attempt any three parts of the following: (3x10=30)

a) What is the role of Milky Way in its Local Group?b) How solar system is thought to be originated? What are the two

important theories of its origin?c) What are dwarf planets? Name and give their characteristics?d) How we can measure the masses of the astronomical bodies?

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e) What factors influence the magnetic fields of a star?Section C

Attempt all questions. All questions carry equal marks (5x10=50)

3. Attempt any two parts of the followinga) How the stars evolve from the main sequence to giants?b) What is Black Hole? How it is formed?c) Discuss the properties source of energy of Active Galactic

Nuclei?

4. Attempt any two of the following: (2X5=10)Write the note on:a) Elliptical galaxyb) Spiral Galaxiesc) Barred spiral galaxyd) Irregular Galaxies

5. Attempt any one of the following: (1X10)a) Explain Hubble expansion model.b) How you can establish the reliability of Chandrasekhar's

formula?

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Model Test Paper-3Note: Attempt all Questions. Total Marks: 100

Section AAttempt all parts of this question. All parts of the question carry equal marks.1. This Question contains 10 objective types/fill in the blank type /

true-false type questions (2X10=20)1) Most of the large objects in orbit round the sun lie near the orbit

of the earth called ___________2) The oldest stars contain few_______, while stars born later

have more.

3) If the bodies are permanently associated, their orbit will be _________. If they are not permanently associated, their orbits will be ____________.

4) Stars with high rates of proper motion are likely to be relatively close to the _______, making them good candidates for parallax measurements

5) Supernova ___________ release an enormous amount of energy both in electromagnetic radiation and in the form of violent stellar wind.

6) Novae remain bright for only __________ or weeks and then gradually fade.

7) _________ matter appears to account for around 90% of the mass of most galaxies

8) Future of the universe depends on ____________ of the matter in the space.

9) Ultra-compact dwarf galaxies have recently been discovered that are only ____________ across.

10) The oldest stars contain few_______, while stars born later have more.

Section B2. Attempt any three parts of the following: (3x10=30)

a) What are the major subfields within astronomy?b) Name the disk like regions of the interplanetary medium?

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c) Consider Kepler’s third law as given in section 4.5, carefully explain why K= 1 when a is measured in astronomical units and p2 in years?

d) What is Spectral Sequence?e) What is Jeans Instability?

Section CAttempt all questions. All questions carry equal marks (5x10=50)

3. Attempt any two parts of the followinga) What is the location of the solar system in the Galaxy? What is

solar system's cosmic year?b) Suppose Kepler’s law applies to the motion of Jupiter’s satellite

Io round that planet, and that one of the satellite has period of 5.196 times as long as another one. What will be the ratio of semimajor axes of their orbits?

c) What is the significance of the spectrum of a star in determining its properties?

4. Attempt any two of the following: (2X5=10)Write the note on:(i) Hydrostatic Equilibrium.(ii) Perfect Gas Law: (iii) Minimum Pressure and Temperature in Stellar Interior.(iv) Thermal Equilibrium.

5. Attempt any one of the following: (1X10)a) What are the different scenarios by which a protostar

condensation may get started?b) How galaxies are classified?

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