Chapter 4

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Chapter 4 Telescopes
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• John Swez
• Instructor
• Physics 360/Geol 360

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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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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.
(2) Astronomy Magazine Sept. 2002 issue defines
the faintest naked eye star at 6.5 apparent
magnitude.
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.
Absolute Magnitude is defined as how bright a
star would appear if it were of certain apparent
magnitude but only 10 parsecs distance.
Magnitude Difference of 1 is 2.5121, 2 is
2.51221 or 6.311, 3 is 2.5123 15.851 etc.
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The Physics of Light
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Later, Diffraction will have a direct link to
resolving power
Left Picture depicts the Relationship of the
Intensity versus the inverse square of the
distance
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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
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An example of the second order bending of light
Left
Credit for photo on lower left http//www.glenbroo
k.k12.il.us/gbssci/phys/Class/light/u12l1a.html
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Both circles in the sky and the bottom circle
look smaller than the circle on the horizon.
How your perception may be fooled.
Indeed all the circles are the same size!
From Explorations An Introduction to Astronomy
3rd ed, Thomas Arny p 123
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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/coor
dinates.html
Angular Measure is Important in Astronomy
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.
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Basics of how a simple refracting telescope works
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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 Schmidt Telescope
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.
11a
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.)
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Resolving Power

• A telescopes 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 gt 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
D is expressed in centimeters (cm) of the
aperture.
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)
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 Strobels 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 p (diameter of
objective)2/4, where the value of p is
approximately 3.1416. For example a
40-centimeter mirror has four times the
light-gathering power as a 20-centimeter mirror
( p402/4) / ( p202/4) (40/20)2 4.
Figure and Text from http//www.astronomynotes.com
/ Nick Strobels 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 Strobels Astronomy Notes
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Why Reflecting Telescopes are Preferred over
Refracting
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• 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
• CCDs 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/pict
ures.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.html
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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.
Hubble Discovers Black Holes in Unexpected Places

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

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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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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Hubble Telescope with corrective optics
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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.

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Credit for picture and text NASA
This color image of Saturn was taken with the
HST's Wide Field and Planetary Camera (WF/PC) in
the wide field mode at 825 A.M. EDT, August 26,
1990, when the planet was at a distance of 1.39
billion kilometers (860 million miles) from
Earth.
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Courtesy for picture and text NASA
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
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Build a Hand Held Hubble http//hubblesite.org/fu
n_.and._games/hand-held_hubble/materials.shtml
Photo and text courtesy of http//hubble.nasa.gov/

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.
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View of a colliding galaxy dubbed the "Tadpole"
(UGC10214) Photo Courtesy NASA Hubble
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Astronomy 360
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• The slides on celestial coordinates may be
  covered at a later date.

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From Astronomy Notes on Web Ref. Noted below.
Learning Celestial Coordinates Part I
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.
Figure from http//csep10.phys.utk.edu/astr161/le
ct/time/coordinates.html
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Celestial Coordinates Cont.
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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/coord
inates.html
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Celestial Coordinates
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.ed
u/sbo/astroinfo/coords/coordinates.html
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.
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More Important The Equatorial Coordinate System
Measurement of "celestial latitude" is given the
name declination (DEC),
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.
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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).
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".
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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.
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.
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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.ed
u/sbo/astroinfo/coords/coordinates.html
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.