Chapter 4 “Telescopes”

John Swez

Instructor

Physics 360/Geol 360

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1. This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version

Men and women have looked up at the sky and wondered about the things they see up there for as long as humans have lived on our Earth. Long ago, the Sun and Moon were mysterious objects that could be seen in the day and night. But the planets and stars were even more mysterious probably because they are so far away that we could only see them as points of light. Unlike the things on the Earth that we can study up close, handle, listen to, smell, and taste, the only thing ancient watchers of the sky had to learn about things in space was their eyes and imaginations. Only very recently in the history of humanity have astronomers been able to extend the reach of our eyes (and our imaginations!).

Galileo pioneered modern explorations in the early 1600's by using a device originally invented for naval operations to explore the heavens. The device he used, of course, was the telescope, an instrument used to gather and focus light. Our atmosphere prevents most of the electromagnetic radiation from reaching the ground, allowing just the visible band, parts of the radio band, and small fractions of the infrared and ultraviolet through. Our eyes can detect the visible (optical) band, so the early telescopes were all built to observe in that part of the electromagnetic spectrum. It wasn't until the 1930's that astronomers began observing with another part of the electromagnetic spectrum---the radio band. The development of space technology has enabled astronomers to put telescopes above the atmosphere and explore all of those places out there using the full range of the electromagnetic spectrum

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Tip of the Day: (1) How sunrise to sunset is defined. Sunrise is time from just when the top of the sun clears the horizon to sunset when the last bit of sun disappears.

“Apparent Magnitude” was defined by Hipparachus in 150 BC. He devised a magnitude scale based on:

Magnitude Constellation Star

1 (Orion) Betelgeuse

2 Big Dipper various

6 stars just barely seen

However, he underestimated the magnitudes. Therefore, many very bright stars today have negative magnitudes.

Magnitude Difference is based on the idea that the difference between the magnitude of a first magnitude star to a 6th magnitude star is a factor of 100. Thus a 1st mag star is 100 times brighter than a 6th mag star. This represents a range of 5 so that 2.512 = the fifth root of 100. Thus the table hierarchy is the following.

Magnitude Difference of 1 is 2.512:1, 2 is 2.5122:1 or 6.31:1, 3 is 2.5123 = 15.85:1 etc.

(2) Astronomy Magazine Sept. 2002 issue defines the faintest naked eye star at 6.5 apparent magnitude.

Absolute Magnitude is defined as how bright a star would appear if it were of certain apparent magnitude but only 10 parsecs distance.

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The Physics of Light

Left: Picture depicts the Relationship of the Intensity versus the inverse square of the distance

Later, Diffraction will have a direct link to resolving power

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Chapter 4, Telescopes

Ability to Focus Bending of Light Index of Refraction

( Dependent)

Collecting Power How Bright! Depends on Collector Area

Resolving Power Two Objects Close Depends on Quality (Ability to Discern) of Collector Area

Magnification Image Size/Object Size

Related Concepts

Atmospheric Refraction The Moon Illusion (page 122, text)

Alteration of the Sunset/Sunrise Time hence the equinox (SAME PAGE)

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More on the Physics of Light

Credit for photo on lower left http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1a.html

An example of the “second order bending of light” Left

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How your perception may be fooled.

From Explorations An Introduction to Astronomy 3rd ed, Thomas Arny p 123

Both circles in the sky and the bottom circle look smaller than the circle on the horizon.

Indeed all the circles are the same size!

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“In order to specify a direction by angular measure, you need to know just how "big" angles are. Here's a convenient "yardstick" to use that you carry with you at all times: the hand, held at arm's length, is a convenient tool for estimating angles subtended at the eye:” It is convenient to remember that the width of your knuckles when the arm is extended out is about 8 degrees. Remember, there are 360 degrees to a full circle.

This slide and is copied verbatim from from the Sommers-Bausch Observatory's "APAS 1010 Laboratories - Introduction to Astronomy" lab manual, 1996, by Keith Gleason. Via website http://lyra.colorado.edu/sbo/astroinfo/coords/coordinates.html

Angular Measure is Important in Astronomy

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Basics of how a simple refracting telescope works

A simple refracting two lens telescope (right) showing aperture objective and eyepiece. (left and below) A diagram depicting chromatic aberration

Images courtesy of Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

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A classical Newtonian reflecting telescope.(Image by Duncan Kopernicki.)

Small reflectors are often in a Newtonian configuration (shown above). They have a paraboloid primary mirror which brings the light of any object in the field of the telescope to a focus near the top end of the tube, called the prime focus. A flat mirror is placed at 45 to the axis of the tube and reflects the light out to an eyepiece at the secondary focus.

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A classical Cassegrain reflecting telescope.(Image by Duncan Kopernicki.)

In the classical Cassegrain telescope the primary mirror takes a paraboloid shape. This brings the light of any object in the field of the telescope to a focus near the top end of the tube, called the prime focus. This is used on big telescopes to take pictures of small areas of the sky. This used to be done using photographic plates but these have largely been replaced by more efficient digital detectors, called Charge Coupled Devices (CCDs).

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Basic Type of Telescopes

Basic Diagram of Schmidt-Cassegrain Technology

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The Horsehead Nebula in Orion. This image, approximately 1.5° across, was obtained with the UK Schmidt telescope at the Anglo-Australian Observatory.(Image Credit: David Malin, Anglo Australian Observatory/Royal Observatory

Edinburgh.)

For photography of large areas of the sky the primary mirror is made with spherical curvature and an aspheric `corrector plate' is placed at the top end of the telescope tube. There are three large Schmidt telescopes in the world with fields about 6° across (the Moon's apparent diameter in the sky is half a degree). The oldest of these is the Palomar Schmidt (not to be confused with the Palomar 200-inch) and the other two are the ESO Schmidt in Chile and the United Kingdom Schmidt in Australia. These have been used to produce photographic charts of the whole sky.

The Schmidt Telescope

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Resolving Power

•A telescope’s ability to resolve two objects (stars) close to each other

•Is limited by the nature of wave light (Diffraction)

•Two points separated by an angle (measured in seconds) cannot be observed as separate sources unless D > 0.02 / where D is the telescope diameter in centimeters, is the wavelength of light in nanometers and is the angle of separation (seconds) [Equation on page 128, text]

• Example: to resolve two stars separated by 0.1 seconds of arc when observing with visible light you need a 1 meter diameter telescope**

•** Unfortunately the atmosphere seriously blurs fine details degrading the resolving power to earth based telescopes to below their diffraction limits

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Mathematical Expression for Resolving Power

Example: Problem 1, page 143. Compare the collecting power of a telescope with a 10 cm (about 4 inch) diameter mirror to that of a human eye. (Take the diameter of the pupil of the eye to be about 5 millimeter)

D is expressed in centimeters (cm) of the aperture.

Solution. Part (a). Telescope. Solve the above equation for to get = 0.02 / D. Then substituting in the numbers solve for (use = 500 nm) = 0.02 (500) / 10 = 1 second of angular separation.

For Part (b). Eye. Again, solve the same equation. = 0.02 500 / .5 = 20 seconds of angular separation. Use this result to also solve Problem 3.

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The pictures clearly show the increase in sharpness as the objective size is increased. The size of each of the blobs is the size of the smallest detail that can be seen with that telescope under ideal conditions. Atmospheric distortion effects (smearing of the binary star images to a blob the size of the entire frame) and obscuration and diffraction by the secondary and its supports are NOT shown here.

Figure and Text from http://www.astronomynotes.com/ Nick Strobel’s Astronomy Notes

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Collecting Power

“The area of the objective is the determining factor. Since most telescope objectives are circular, the area = × (diameter of objective)2/4, where the value of is approximately 3.1416. For example: a 40-centimeter mirror has four times the light-gathering power as a 20-centimeter mirror [( 402/4) / ( 202/4) = (40/20)2 = 4]. “

Figure and Text from http://www.astronomynotes.com/ Nick Strobel’s Astronomy Notes

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Magnifying Power (not discussed in detail in text)

“The ability of a telescope to enlarge images is the best-known feature of a telescope. Though it is so well-known, the magnifying power is the least important power of a telescope because it enlarges any distortions due to the telescope and atmosphere. A small, fuzzy faint blob becomes only a big, fuzzy blob. Also, the light becomes more spread out under higher magnification so the image appears fainter! The magnifying power = (focal length of objective) / (focal length of eyepiece); both focal lengths must be in the same length units. A rough rule for the maximum magnification to use on your telescope is 20 × D to 24 × D, where the objective diameter D is measured in centimeters. So an observer with a 15-centimeter telescope should not use magnification higher than about 24 × 15 = 360-power. “

Figure and Text from http://www.astronomynotes.com/ Nick Strobel’s Astronomy Notes

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Why Reflecting Telescopes are Preferred over Refracting

• A large mirror can be thin but a large lens must be thicker thus heavier.

• A lens has two surfaces that must be cleaned and polished; a mirror only has one;.

• Glass absorbs light! The thicker the light the more absorption.

• Lenses need to be supported only around the outside; mirrors can be supported by the back

• For large lenses, glass deforms under its own weight; thus changing the lenses’ properties.

• In a lens, different colors are refracted by different amounts. (Chromatic Aberrations). Lenses are corrected for chromatic aberrations and are called achromats.

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Recording Images

•For many years the naked eye was used; sketches were produced

•Photographic Film became in use about the turn of the last century

•Low efficiencies occur with photographic film (~ 4%, thus much patience must be spent with clock drive mechanisms)

•CCD (Charge coupled detector arrays) are used today with efficiencies of 75%

•CCD’s are used in digital cameras today

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Advances in Observing

Observing in the Infrared, UV, Gamma Rays and Radio Waves

The Hubble Space Telescope (public pictures at) http://oposite.stsci.edu/pubinfo/pictures.html

The Chandra X-ray Observing Telescope

We (students and teachers) can observe

The personal computer

Image Processing

Interferometer Telescopes (resolution is not set by the size of the individual mirrors but by their distance of separation (the 100 x 100 rule); exp. Twin Keck telescopes

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http://oposite.stsci.edu/pubinfo/pictures.html20

Hubble Discovers Black Holes in Unexpected Places

The black hole in globular cluster M15 [left] is 4,000 times more massive than our Sun. G1 [right], a much larger globular cluster, harbors a heftier black hole, about 20,000 times more massive than our Sun.

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Stargazers Pub at http://www.stargazers-pub.net gives a very nice treatment of telescopes; especially if you are interested in purchasing one.

•If you're thinking of buying a telescope, the best way to choose one is to go to a local astronomy club meeting or star party. Most clubs have public viewing evenings every month, and these are most helpful to the interested newbie. Nothing beats actual experience with a variety of scopes when you're trying to decide what to spend your money on.

•Try to stay away from 'department store' telescopes. You know, the ones you find a the local SUPERSTORE (I'm not going to name names, but we all know the kinda stores I'm talking about..). They usually come in brilliantly colored boxes with amazing pictures of Saturn and the Andromeda Galaxy on the top and claim to be able to magnify your views by 500x or more. They might look nice on the shelf, but do a little more research into telescope buying & optics before you shell out for one of these snoozers. You're *MUCH* better off saving your money for another couple months and buying a scope from a reputable astronomical company, such as Orion, Celestron, or Meade.

•Etc.

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10-meter Keck Telescope at the W.M. Keck Observatory.

1. This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

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This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for

the updated and corrected version.

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The Very Long Baseline Array is a huge interferometer that uses ten telescopes placed in sites from Hawaii to the Virgin Islands. This telescope is the 8,600 kilometers across and has a resolution as good as 0.0002 arc second! With a resolution about 50 times better than the Hubble Space Telescope, it is able to detect features as small as the inner solar system at the center of our galaxy, about 26,000 light years away.

This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

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1. This page was copied from Nick Strobel's Astronomy Notes. Go to his site at

www.astronomynotes.com for the updated and corrected version.

Radio Telescope Image (Top) and Visible Image (below)

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“The Hubble Space Telescope orbits far above the distorting effects of the atmosphere, about 600 kilometers above the Earth. This perch gives astronomers with their clearest view ever, but it also prevents them from looking directly through the telescope. Instead, astronomers use Hubble's scientific instruments as their electronic eyes.” Upper Left: Closer View

Photo and text courtesy of http://hubble.nasa.gov/

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M 100 a few days before (left) and after (right) the corrective optics (COSTAR) were installed in December 1993.

1. This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

Hubble Telescope with corrective optics28

“This color image of Saturn was taken with the HST's Wide Field and Planetary Camera (WF/PC) in the wide field mode at 8:25 A.M. EDT, August 26, 1990, when the planet was at a distance of 1.39 billion kilometers (860 million miles) from Earth.”

Credit for picture and text: NASA29

“This enlargement of the Saturn image reveals unprecedented detail in atmospheric features at the northern polar hood. Saturn's north pole is presently tilted toward Earth by 24 degrees”

Courtesy for picture and text: NASA

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NASA's Hubble Space Telescope has obtained the clearest pictures ever of our solar system's most distant and enigmatic object: the planet Pluto. The observations were made with the European Space Agency's Faint Object Camera.

Photo and text courtesy of http://hubble.nasa.gov/

Build a Hand Held Hubble: http://hubblesite.org/fun_.and._games/hand-held_hubble/materials.shtml

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View of a colliding galaxy dubbed the "Tadpole" (UGC10214): Photo Courtesy NASA Hubble

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Astronomy 360

The slides on celestial coordinates may be covered at a later date.

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Learning Celestial Coordinates: Part I

Figure from: http://csep10.phys.utk.edu/astr161/lect/time/coordinates.html

Study pages 65 – 67 in your text (Thomas T Amy); in particular the section on “Celestial Coordinates”

“In the celestial coordinate system the North and South Celestial Poles are determined by projecting the rotation axis of the Earth to intersect the celestial sphere, which in turn defines a Celestial Equator. “ **

From Astronomy Notes on Web; Ref. Noted below.

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Celestial Coordinates: Cont.

“The celestial equivalent of latitude is called declination and is measured in degrees North (positive numbers) or South (negative numbers) of the Celestial Equator. The celestial equivalent of longitude is called right ascension. Right ascension can be measured in degrees, but for historical reasons it is more common to measure it in time (hours,

minutes, seconds): the sky turns 360 degrees in 24 hours and therefore it must turn 15 degrees every hour; thus, 1 hour of right ascension is equivalent to 15 degrees of

(apparent) sky rotation. “ from http://csep10.phys.utk.edu/astr161/lect/time/coordinates.html

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“The alt-azimuth (altitude - azimuth) coordinate system, also called the horizon system, is a useful and convenient system for pointing out a celestial object. One first specifies the azimuth angle, which is the compass heading towards the horizon point lying directly below the object. Azimuth angles are measured eastwardly from North (0 deg azimuth) to East (90 deg), South (180 deg), West (270 deg), and back to North again (360 deg = 0 deg). The four principle directions are called the cardinal points. Next, the altitude is measured in degrees upward from the horizon to the object. The point directly overhead at 90 deg altitude is called the zenith. The nadir is "down", or opposite the zenith. “

This slide and the next six slides are copied verbatim from from the Sommers-Bausch Observatory's "APAS 1010 Laboratories - Introduction to Astronomy" lab manual, 1996, by Keith Gleason. Via website http://lyra.colorado.edu/sbo/astroinfo/coords/coordinates.html

Celestial Coordinates36

More Important: The Equatorial Coordinate System

“ If we extend the Earth's axis outward into space, its intersection with the celestial sphere defines the north and south celestial poles; equidistant between them, and lying directly over the Earth's equator, is the celestial equator. Measurement of "celestial latitude" is given the name declination (DEC), but is otherwise identical to the measurement of latitude on the Earth: the declination at the celestial equator is 0 deg and extends to ±90 deg at the celestial poles. “

Measurement of "celestial latitude" is given the name declination (DEC),

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“The east-west measure is called right ascension (RA) rather than "celestial longitude", and differs from geographic longitude in two respects. First, the longitude lines, or hour circles, remain fixed with respect to the sky and do not rotate with the Earth. Second, the right ascension circle is divided into time units of 24 hours rather than in degrees; each hour of angle is equivalent to 15 deg of arc

The Earth orbits the Sun in a plane called the ecliptic. From our vantage point, however, it appears that the Sun circles us once a year in that same plane; hence, the ecliptic may be alternately defined as "the apparent path of the Sun on the celestial sphere".

“The ecliptic crosses the equator at two points; the first, called the vernal (spring) equinox, is crossed by the Sun moving from south to north on about March 21st, and sets the moment when spring begins. The second crossing is from north to south, and marks the autumnal equinox six months later. Halfway between these two points, the ecliptic rises to its maximum declination of +23.5 deg (summer solstice), or drops to a minimum declination of -23.5 deg (winter solstice). “

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“As with longitude, there is no obvious starting point for right ascension, so astronomers have assigned one: the point of the vernal equinox. Starting from the vernal equinox, right ascension increases in an eastwardly direction until it returns to the vernal equinox again at 24 h = 0 h.

The Earth precesses, or wobbles on its axis, once every 26,000 years. Unfortunately, this means that the Sun crosses the celestial equator at a slightly different point every year, so that our "fixed" starting point changes slowly - about 40 arc-seconds per year. Although small, the shift is cumulative, so that it is important when referring to the right ascension and declination of an object to also specify the epoch, or year in which the coordinates are valid. “

“The fundamental purpose of all timekeeping is, very simply, to enable us to keep track of certain objects in the sky. Our foremost interest, of course, is with the location of the Sun, which is the basis for the various types of solar time by which we schedule our lives. “

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“Time is determined by the hour angle of the celestial object of interest, which is the angular distance from the observer's meridian (north-south line passing overhead) to the object, measured in time units east or west along the equatorial grid. The hour angle is negative if we measure from the meridian eastward to the object, and positive if the object is west of the meridian.

For example, our local apparent solar time is is determined by the hour angle of the Sun, which tells us how long it has been since the Sun was last on the meridian (positive hour angle), or how long we must wait until noon occurs again (negative hour angle).

If solar time gives us the hour angle of the Sun, then sideral time (literally, "star time") must be related to the hour angles of the stars: the general expression for sidereal time is Sidereal Time = Right Ascension + Hour Angle which holds true for any object or point on the celestial sphere. It's important to realize that if the hour angle is negative, we add this negative number, which is equivalent to subtracting the positive number. “

This slide and the previous six slides are copied verbatim from from the Sommers-Bausch Observatory's "APAS 1010 Laboratories - Introduction to Astronomy" lab manual, 1996, by Keith Gleason. Via website http://lyra.colorado.edu/sbo/astroinfo/coords/coordinates.html

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