Science 3210 001 : Introduction to Astronomy

Lecture 2 : Visual Astronomy -- Stars and Planets

Robert Fisher

Items

Course adds

The course had been booked to capacity, but I will be adding as many people as the room can accommodate, in the order I have received requests.

People who attended last week’s lecture Natasha Shah Amanda Mayfield Simon Spartalian

Add/drop day is February 6th. This means today is the last day where I am generally available to sign add/drop cards.

Course webpage has been updated with first week’s lectures, and the first reading and homework assignment : http://flash.uchicago.edu/~rfisher/saic.html

Questions -- seek and ye shall find!

Review of Lecture 1

History of Astronomy Ancient Astronomy Advent of Natural Philosophy Medieval Astronomy in Arab World Birth of Modern Science

Science Overview Scales in the Cosmos Cosmic Calendar Powers of Ten Video

Overview of Lecture 2

I. The Celestial Sphere

II. The Stars

IiI. The Motion of the Planets

Important Lessons to be Learned Today

Because the stars are very distant, their motion on the sky is well-described as if they revolved around the Earth

The motion of the planets is significantly more complex, and required elaborate geometrical constructions in the ancient geocentric system due to Ptolemy

Niklaus Copernicus simplified matters tremendously by putting the sun at the center of the universe -- even though he lacked the “smoking gun” evidence to prove his case

Motion of the Stars

The foundation of all visual astronomy is a simple fact : the Earth is a Sphere

While common knowledge today, determination of the shape of the Earth was a significant challenge to ancient peoples

The most convincing elementary argument comes from the fact that the Earth’s shadow (as seen in lunar eclipses) is always circular, as Aristotle correctly deduced

Earth Image, Apollo 17 Crew

Lunar Eclipse

The Earth as the Center of the Universe

Looking up at the night sky, it appears as if the entire Universe revolves around the Earth.

QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

Celestial Sphere, Zenith, Nadir, Horizon

The distant stars appear to lie on a solid sphere, the celestial sphere.

The zenith is the direction directly upwards.

The nadir is the direction directly downwards.

The horizon splits the celestial sphere in half along the zenith-nadir axis.

Zenith and Nadir Depend on Your Location

The zenith and nadir directions depend on where one stands on the Earth.

Rotation of the Earth

Motion of the Celestial Sphere

The rotation of the Earth causes the celestial sphere to appear to revolve.

The north/south celestial poles correspond to the north/south poles of the Earth’s rotational axis.

The Motion of the Sun

At a given location, the sun rises towards the east and sets towards the west.

A sundial gnomon casts a shadow away from the sun, towards the west.

The invention of the gnomon is attributed to the ancient Greek philosopher Animaxander, successor to Thales

Determining North from the Sun’s Motion

At noon, the sun reaches its highest point in the sky, directly north.

This was a common method used by the ancients to determine North.

Clockwise

Clockwise

Imagine one wanted to read a sundial. We are facing south.

In the morning, the sun rises in the east, casting a shadow in the west.

In the afternoon, the sun begins to set in the west, casting a shadow to the east, following the same circular arc traced in the morning.

The direction traced by the sun’s shadow in its arc, facing south, is clockwise.

When mechanical clocks with hands were first made, they were constructed so as to rotate in the same sense as the sundial -- clockwise -- not counter-clockwise.

Describing the Celestial Sphere -- The Great Circle

A great circle on a sphere divides the sphere into two hemispheres.

One can imagine the equator as an example of a great circle, but any circle dividing the sphere is a great circle.

Great circle

Describing the Celestial Sphere -- Great Circles

Great circles

Any of the circles in the figure above are examples of great circles.

Angles

Separation between two points on the celestial sphere are measured in terms of angles -- much like a clock.

A full circle is 360 degrees.

Each degree is 60 minutes. The full moon is roughly one-half degree in width.

By remarkable circumstance, the width of the sun is also one-half degree.

Each minute is 60 seconds -- sometimes referred to as arcseconds.

The Meridian

The great circle on the celestial sphere found by connecting north and south and passing through the zenith is referred to as the meridian.

When a celestial body crosses the meridian, it is said to transit.

When a body transits, it reaches its highest point from the horizon.

The terms “AM” and “PM” derive their meaning from the meridian : AM = Ante-Meridian PM = Post-Meridian

The North Celestial Pole and Circumpolar Stars

Looking north from Chicago at night, one can see the North Celestial Pole.

The North Celestial Pole is the direction along which the Earth’s axis is aligned.

The stars which immediately surround the pole never set beneath the horizon. They are called circumpolar stars.

Star Trails Over Mauna Kea, Hawaii

Angles on a Familiar Sphere

Before describing the celestial sphere in more detail, it helps to recall the layout of a more familiar sphere -- the Earth.

On the Earth, angle north or south of the Equator is marked off by latitude.

Angle around the Earth from West to East is marked off by longitude.

Daily Motion of the Stars

The daily motion of the stars Is very simple.

The celestial sphere makes one full circle about the Earth, once per day.

The circle is determined by only angle -- the declination, directly analogous to latitude on the Earth.

Question

In the Northern hemisphere, the stars rise in the East, set in the West, and revolve counter-clockwise around the North celestial pole. In the southern hemisphere the stars rise in the

A) East, set in the West, and revolve counter-clockwise around the South celestial pole.

B) East, set in the West, and revolve clockwise around the South celestial pole.

C) West, set in the East, and revolve clockwise around the South celestial pole.

D) West, set in the East, and revolve counter-clockwise around the South celestial pole.

View from North Pole

At the north pole, the zenith is the north celestial pole.

The nadir is the south celestial pole.

The horizon is the celestial equator.

Precisely half of the celestial sphere is visible.

All stars are circumpolar.

View from Equator

The zenith is the celestial equator.

The north celestial pole always appears directly north.

The full sky is visible -- each star rises for 12 hours each day.

View from Chicago

The altitude of the north celestial pole is equal to the latitude of your position on the Earth - roughly 42 degrees for Chicago.

Stars within 42 degrees of the north celestial pole are circumpolar.

Stars within 42 degrees of the south celestial pole are not visible.

Summary of Celestial Sphere Viewed fom Earth

Question

The celestial equator is :

A) The path of the sun compared with the stars.

B) The path of the moon compared with the stars.

C) The average path of planets on the sky.

D) Always directly overhead at the Earth’s equator.

E) Always along the horizon at the Earth’s equator.

Constellations

Constellations are the “states” on maps of the celestial sphere.

Each region of the sky belongs to precisely one constellation.

Stars within each region are alphabetically named, starting with the brightest stars, by a greek letter followed by the constellation name -- eg, Polaris is Alpha Ursae Minoris.

The Ecliptic

The sun appears to move along a plane in the sky referred to as the ecliptic.

The other planets also appear to move close to the ecliptic.

Physically, the fact that all solar system bodies lie close to the ecliptic is because the entire solar system lies within a flattened disk.

The Plane of The Ecliptic From Fire Island

The Solstices and Equinoxes

The solstices occur when the sun reaches a maximum (solstice = sol sistere or sun stops in Latin) distance away from the celestial equator -- roughly June 21 and December 21.

The equinoxes occur when the sun intersects the celestial equator -- roughly March 21 and September 21. On this day, the sun appears directly above the equator, and every point on earth has equal day and night.

Earth on Equinoxes

Yearly Sky and Zodiac

As the sun moves through the ecliptic, different portions of the night sky become observable.

The ecliptic falls into 12 constellations over the year -- the zodiac.

Angle of Inclination of Earth

The ecliptic makes an angle of 23.5 degrees with the celestial equator.

Physically, this means the Earth’s rotational axis is tilted with respect to its orbit.

Angle of Inclination

As the Earth orbits around the sun, the angle of inclination remains the same.

Origin of Seasons

The angle of inclination causes seasonal variation on Earth.

Question

The ecliptic makes its smallest angle with the southern hemisphere during the

A) Summer

B) Autumn

C) Winter

D) Spring

Private Universe

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Lunar Phases

The appearance of the moon varies over the course of the month.

Eclipses

The lunar orbit is inclined by 5 degrees relative to that of the Earth/sun.

Solar eclipses can occur during the new moon, but only when the sun, moon, and Earth happen to line up.

Similarly, lunar eclipses can occur during the full moon, but only when the sun, Earth, and moon happen to line up.

Lunar Eclipses

The moon passes through the shadow of the Earth.

Light is fully blocked in the umbra, and only partially blocked in the penumbra.

Types of Lunar Eclipses

Three types of Lunar eclipses.

Lunar Eclipses

Question

What would a total lunar eclipse look like to an observer standing on the surface of the moon facing the Earth?

Lunar Eclipses from Moon

Solar Eclipses

Solar eclipses occur when the sun’s light is blocked by the moon.

In a sense, they are completely serendipitous : the sun is 400 times larger than the moon, but is also 400 times further away.

Hence, the apparent angular size of both the moon and the sun are nearly identical.

Solar Eclipses

Three types of solar eclispes can occur.

August 11, 1999 Eclipse Viewed from Mir

The Eclipse of May 28, 585 BC

Thales of Miletus is said to have predicted a remarkable solar eclipse on May 28, 585 BC.

Of this occasion, Herodutus writes, ‘On one occasion [the Medes and the

Lydians] had an unexpected battle in the dark, an event which occurred after five years of indecisive warfare: the two armies had already engaged and the fight was in progress, when day was suddenly turned into night. This change from daylight to darkness had been foretold to the Ionians by Thales of Miletus, who fixed the date for it within the limits of the year in which it did, in fact, take place…The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on.’

One must wonder -- how was it possible for Thales to predict the eclipse?

Solar Eclipses, 1999 - 2020

Both lunar and solar eclipses recur with a frequency of 18 years, 11 days, known as the Saros cycle.

The Saros cycle was known to the ancient Babylonians, and may have been used by Thales to predict the eclipse of May 28, 585 BC.

Why are Eclipses so Rare?

For a total lunar or solar eclipse to occur, there must be a precise alignment of the Sun, Earth, and moon.

However, because of the inclination of the moon’s orbit with respect to the plane of the ecliptic, such alignments are rare.

The Planets

The Motion of Planets

Like the stars, the planets are generally seen to traverse the sky.

Unlike the stars, occasionally the planets are observed to stop and move from west-to-east in so-called retrograde motion.

This behavior gave rise to the ancient greek name -- “planets” comes from a Greek root meaning “wanderer”.

A fully satisfactory explanation of this motion was not developed until Newton.

The Earth as the Center of the Universe

Looking up at the night sky, it appears as if the entire Universe revolves around the Earth.

QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

Geocentric Model of the Universe

This observation led the ancients to formulate a geocentric model of the universe, with the Earth at the center, and the Sun, planets, and stars all revolving around the Earth along spheres.

Cacophony in the Celestial Harmony -- The Problem of Retrograde Motion

The geocentric model of the universe works very well for stars, but there is a major problem for planetary motion.

Occasionally, the outer planets will appear to slow down, stop, then reverse their direction on the night sky -- retrograde motion.

Retrograde Motion

The mystery of retrograde motion can be simply explained in a model with the Sun at the center of the Solar system.

An inner body (like the Earth) is moving more rapidly than an outer body (like Mars), and so will “pass” it much like a faster car on the expressway.

During this passing, the outer planet will execute retrograde motion.

Retrograde Motion in the Geocentric Model --Epicyclic Motion

Explaining retrograde motion in the geocentric model of the universe, however, is almost impossible, unless one invents an additional circular motion which each planet executes, called epcicyclic motion.

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Ptolemaic Model of the Solar System

The ancient astronomer Ptolemy (90 - 168 AD) created the most complex version of the geocentric model of the system, which was used for almost one and a half millenia.

In the Ptolemaic model, the moon, sun, and planets all revolved in circles, which themselves revolved around circles around the Earth.

And in fact, the Earth was not quite at the center of this model, either.

Why Did the Ancients Reject a Heliocentric Model of the Solar System?

In the heliocentric model, due to the motion of the Earth about the sun, the motion of the nearest stars should appear to vary with respect to the more distant stars.

This effect is called parallax.

The ancients attempted to measure this effect, but failed. In fact, because the stars are so distant, it is only detectable with telescopic measurements.

The Heliocentric World View

Niklaus Copernicus was a 16th century scholar and cleric, who wrote treatises in a number of fields.

He is best remembered today for his revolutionary astronomical ideas.

Niklaus Copernicus (1473-1543)

The Copernican Model

Copernicus summarized his model by the following bold (and remarkably valid) assumptions :

1.There is no one center of all the celestial circles or spheres. 2.The center of the earth is not the center of the universe, but only of

gravity and of the lunar sphere. 3.All the spheres revolve about the sun as their mid-point, and therefore the

sun is the center of the universe. 4….the distance from the earth to the sun is imperceptible in comparison with

the height of the firmament. 5.Whatever motion appears in the firmament arises not from any motion of

the firmament, but from the earth's motion. 6.What appear to us as motions of the sun arise not from its motion but from

the motion of the earth and our sphere, with which we revolve about the sun like any other planet.

7.The apparent retrograde and direct motion of the planets arises not from their motion but from the earth's. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

Phases of Venus

In 1610, Galileo used the telescope to observe the phases of Venus for the first time from the Earth.

The phases only made sense if Venus orbited the Sun, not the Earth.

This proved to be a “smoking gun” in favor of the heliocentric model.

Next Week

I) Planetary Motion A) Tycho Brahe and Johannes Kepler B) Kepler’s Laws

II) Physics of Motion A) Galileo and the Physics of Kinematics B) Newton and Newton’s Laws of Motion

II) Physics of Matter and Light