The Scale of the Cosmos

The Celestial Sphere, the 
     Sky, and the Calendar

Archeoastronomy and 
     ancient Sky Viewers

the Copernican Revolution
     (Ptolemy, Copernicus: 
        Models of the Universe)

Pre-telescope astronomy
        including Tycho Brahe

The Origin of Modern
     Astronomy:
     Kepler, 
     Galileo,
     & Newton

Cycles in the Sky:
    Earth, Sun, and Moon 
    (reasons for the seasons)
    (phases, eclipses, tides)
          and the Sky

Atoms and Starlight:
    Interaction of light and matter 
         (a gentle introduction to atomic
          physics)
    Interaction of light and the 
       atmosphere

Astronomical Tools:
    Optical Telescopes, 
    Radio Telescopes, 
    Spectrascopes,
    Modern techniques

Satellite Astronomy
 

Introduction to the Course

Tour of the Universe

 -- our Earth, Moon, individual planets, the solar system, nearby stars, and star clusters, the Milky Way galaxy, the Local Group, and galaxy clusters and superclusters (know their sizes in ascending order and their general appearance)

•  13-20 billion years age of the universe
•  relationship between speed, distance, and time

•  speed of light:  c = 3x10⁵ km/sec
•  astronomical length scales
Astronomical Unit (A.U.) = avg. distance between Earth  and Sun 
= 1.5x10⁸ km
Light Year (l.y.) = distance traveled by light in one year 
= 10¹³ km
• scientific notation and powers of Ten

  10¹² = 1,000,000,000,000      trillion  tera-
  10⁹ =        1,000,000,000        billion   giga-
  10⁶ =               1,000,000        million  mega-
  10⁵ =                  100,000
  10⁴ =                    10,000
  10³ =                       1000        thousand  kilo-
  10² =                         100
  10¹ =                           10
  10⁰ =                             1
  10^-1 =                        0.1
  10^-2 =                      0.01         centi-
  10^-3 =                    0.001         milli-
  10^-4 =                  0.0001
  10^-5 =                0.00001
  10^-6 =              0.000001         micro-
  10^-9 =        0.000000001        nano-
  10^-10 =    0.0000000001meter      Angstrom (Å)
(be able to do calculations using scientific notation)

• Increasing length scales (x100 each step):

 -- 1 mm: size of an ant
 -- 10 cm: size of a flower
 -- 10 m: size of a boxing ring or ~10 yards on a football field
 -- 1 km: several dozen city blocks or ~5/8 of a mile
 -- 100 km: distance from here to Panama City Beach for spring break
 -- 10,000 km: almost the size of the Earth
 -- 1,000,000 km: just over the diameter of the Moon's orbit
 -- 10⁸ km: ²/₃ the radius of the Earth's orbit; light takes 5 minutes to cross
 -- 10¹⁰ km: essentially the size of the solar system
 -- 10¹² km: the Sun a tiny dot, mostly empty space
 -- 10¹⁴ km: nearest half dozen stars, 10 light years across
 -- 10¹⁶ km: small fragment of the Milky Way galaxy, ~1000 stars
 -- 10¹⁸ km: entire galaxy, 100,000 light years, 100 billion stars
 -- 10²⁰ km: much larger than the Local Group of galaxies
 -- 10²² km: one billion light years, incl. most of the observable universe, Quasars
 -- 10²⁴ km: 100 billion light years; no light has yet traveled that far; well beyond the edge of the visible universe

The Celestial Sphere, the Sky, and the Calendar

What you need to know:
     * features of the celestial sphere
     * definition of the celestial equator, poles, meridian, zenith, nadir, etc.
     * definition of angular diameter, ecliptic, zodiac
     * the reasons for the season
     * cause and appearance of eclipses and phases of the moon.
 

NOTE THE DIFFERENCES:

"local" coordinate system based on the observer's horizon (altitude, azimuth) and a "global" coordinate system fixed to the celestial sphere, and thus also to the stars (right ascension, declination)

ALTITUDE  0° (horizon)  to +90° (straight up)
AZIMUTH  0° (north) to 360° (around horizon eastward)

LATITUDE: North-south position on Earth
      South Pole -90°; Equator 0°; North Pole +90°
     * In the northern hemisphere, Latitude is equal to the altitude (height above the horizon) of the North Celestial Pole (position of Polaris).
LONGITUDE: East-west position on the Earth
     -180° (west) to  +180° (east)
      0° through Greenwich, England
      * Longitude can be obtained by knowing the precise time that a star of known right ascension passes across the local meridian line and comparing that withe  the exact time that the same star crossed the Greenwich meridian.

ZENITH: straight up, direct overhead
NADIR: straight down, directly under your feet
MERIDIAN: curved arc on the celestial sphere through North Pole, Zenith, and South Pole.

DECLINATION:  North-south position on the celestial sphere (fixed to the sphere)
   -90°    to     +90°
     Celestial South Pole -90°
     Celestial Equator        0°
     Celestial North Pole +90°
RIGHT ASCENSION:  East-west position on the celestial sphere (fixed to the sphere)
   0hr    to     24hr 

NOTICE: the relative elevation of the Sun at noon at different times of the year as it moves along the ecliptic.

ECLIPTIC (ZODIAC): path of the Earth's orbit around the Sun; apparent path of the Sun across the sky.  The Zodiac is that band of constellations through which the ecliptic passes, and through which all the planets (with orbits near the ecliptic) move.

Reasons for the Seasons
VERNAL EQUINOX
SUMMER SOLSTICE
AUTUMNAL EQUINOX
WINTER SOLSTICE
     Know what each is.

PRECESSION: 25,800 year cycle of the wobble of the Earth's rotation axis; NCP now pointed at Polaris, but in 3000 B.C. it was pointed at Thuban (a-Draconis), and will continue to sweep across the sky.

NOTICE: the relative positioning of the Sun, Earth, and Moon and the planets as they move through these motions.

ECLIPSES:  Solar, Lunar, Umbra, Penumbra
PLANETARY MOTION:  Direct and Retrograde

• Constellations
• Magnitude Scale
• Motion

The Ancients were keen observers of the sky, and guided their lives by the cycles they saw.

 *  cycles of day and night -- rotation of the earth.
 *  cycles of the tides and fishing and commerce -- relative position of the Earth, Moon and Sun, and the cycles of days and months.
 *  cycles of the months and women's monthly cycles.
 *  cycles of the seasons and the planting and harvesting of crops.
 *  etc., . . .

. . . and with good reason.
(Life throughout history has nearly always been at or near the subsistence level -- right at the boundary between life and death, between survival and catastrophe.)

 *  work when it's light, rest when it's not.
 *  pragmatism; as a boatman, you could only get in and out of most  harbors safely at high tide, and wanted to be where the fish were when they were running. further it was always important not to run ships aground on shallow shoals.   All these depended on knowing the cycles of the tides.
 *  plant and harvest crops in favorable seasons; if you plant too soon or too late, your crops will fail and   you will all die.

. . . but superstition grew up around all these activities.  These were life-and-death matters to them! This lead to. . .
 

Ancient religions

    -- examples: 
          Egyptian planting cycles set to the co-rising of Sirius with the Sun.
          Stonehenge, Mayans, American Indian stone circles, etc. -- the ancients were exceptionally keen observers of the sky, set very precise geometrical observatories where they set their calendars by aligning with the stars, and motions of the planets and the Sun.
 

Astrology

    -- Many careful scientific studies have shown no correlation between astrological birth sign and events or patterns in people's life.

Geocentric Model of the Universe
Claudius Ptolemius, Greek scholar and librarian living  in Alexandria Egypt 140 AD
Earth centered

 *  based on the Aristotelian world view that the world followed patterns of symmetry and truth and beauty
 *  tied very closely to the Christian view of the centrality and importance of Man in the universe
 *  perfectly circular orbits
 *  cycles upon cycles upon cycles (epicycles and deferents)
 *  required great complexity to explain retrograde motion.
 

Heliocentric Model of the Universe
Nicholas Copernicus, Polish astronomer (b. 1473)
Sun-centered

 *  radical new view of the heavens.
 *  strictly against Christian (Roman Catholic) doctrine, heretical.
 *  still circular orbits
 *  explained retrograde motionmuch more simply and elegantly.
 *  was in fact much less precise in finding the exact positions of the planets than earlier models.
 

_*  Ancient (pre-telescope) Observers:
  -- The ancients were exceptionally keen observers of the sky, set very precise geometrical observatories where they set their calendars by aligning with the stars, with motions of the planets, and with the Sun. (e.g. Egyptian planting cycles set to the co-rising of Sirius with the Sun; Stonehenge; Mayans, American Indian stone circles, etc. 

  -- Erastosthenes: (Greek living in Egypt, 273 B.C.) measured quite precisely the size (circumference) of the Earth using gnomon, angles, and the paced distance between Alexandria and Syene.

   -- Tycho Brahe: greatest pre-telescope observational astronomer; Danish nobleman; measured very precisely the positions of the planets for over a period of 30 years; Johannes Kepler was his assistant and used Tycho's data to generate his (Kepler's) three laws.

What you need to know:
-- contributions of Tycho, Kepler, Copernicus, Galileo, and Newton, and about when they lived
-- Kepler's laws and their use.
-- how Galileo's observations could be used to prove Copernican model of the universe.
--  why Newton should be considered the greatest thinker of all time.


 

• Kepler, Galileo, Newton, and Edmund Halley (who was Astronomer Royal to the British crown, and Newton's good friend) were all overlapping contemporaries with Tycho Brahe and many of the historical "movers and shakers" of the 17th century.

  -- "wandering mathematician;" assistant to Tycho Brahe.
  -- published Rudolphian tables of planetary motions; 
  --  also both Tycho and Kepler observed and studied separate supernovas (which were the last supernovae seen in this galaxy, and the last seen up close until SN1987A).

Kepler's three Laws of Planetary Motion:

• Kepler's First Law

"The orbits of the planets are ellipses with the sun at one focus."
eccentricity -- elongation of orbit
 
• Kepler's Second Law

"A line from the planet to the sun sweeps over equal areas in equal intervals of time."
 
• Kepler's Third Law

"A planet's orbital period squared is proportional to its average distance from the sun cubed."
P²(yrs) = A³(AU) _{/(m1 +m2)(multiples of the Sun's mass)}
        or
P²(sec) = 4p² x A³(meters)/_{G x (m1+m2)(kilograms)}
where G = 6.67x10^-11m³/_kg._sec2
where P is the period (time of one cycle) and A is the semimajor axis of the elliptical orbit (which is the average radius of the orbit).

and in the special case where the sun is at the center of the motion:
P²(yrs) = A³(AU)


These laws are entirely observational - they tell 'how' the planets move in their orbits, but not 'why'. It wasn't until Newton's laws that the 'why's started to be answered.

 

-- "Father of Modern Astronomy," and in fact also the father of much of the modern scientific method.   -- born in Pisa, Italy in 1564, and active and devout Catholic.   -- Very important as an observational astronomer. He was the first man to use telescope extensively to observe the heavens.    * observed the mountains and craters on the Moon.   * first to observe sunspots.   * first to the rings of Saturn.   * observed four largest moons of Jupiter,  which was strong proof that orbital motion can be centered on some other object than the Earth, and that planets can have satellite systems.   *observed the phases and range of sizes of Venus, which is only explainable if Venus is orbiting the Sun rather than orbitting the Earth.   -- He was strong advocate of Copernicus' heliocentric model of the universe, and probably the single person whose observations 'proved' that model more strongly than any other.

actual drawings from  Galileo's observations  of the moons of Jupiter

  -- He lived and worked in Italy (for a long time was a professor at the University of Pisa) and because he was so close to the seat of the Catholic church at Rome, was persecuted as a heretic for his views.
  -- forced by Catholic church to recant his support for his Copernican views; died after over ten years under church-imposed house arrest on Jan. 8, 1642.

• Life and Works:

  -- born December 25, 1642 in rural English village of Woolsthorpe.
  -- very well educated; studied physics and mathematics at Trinity College, Cambridge University.
  -- spent much of his adult life living almost in isolation as a country gentleman, specifically to avoid the Black Plague that was ravaging London and many of the cities of Europe at the time.
  -- probably the single greatest thinker of all time. Single-handedly did more to advance a broader range of widely divergent areas of science than anyone else who has ever lived.
  -- advanced studies in:

  * Optics: developed ways of describing the path and interactions of light, developed an entirely new type of telescope (which now carries his name). 
  * Physics: developed three laws of motion.
  * Mathematics: invented differential calculus.
  * Astronomy: developed the Law of Universal Gravitation; used it to predict the return of Halley's comet.

  -- greatest written work was Principia Mathematica, published in 1687 (in Latin) which included his law of gravitation, his laws of motion, and much else.
  -- placed science on firm analytical basis -- mathematically showed "why" the planets move in their orbits and how those motions are related to the motions of al other objects, even those as simple as an apple falling from a tree.
 
• Gravity and Motion

Newton's Three laws of Motion:
   1. inertia: a body at rest tends to remain at rest, or if in motion tends to remain in uniform linear motion unless acted upon by a force.
   2. F = ma: acceleration (change in motion) proportional to force applied.
   3. action-reaction: when two bodies interact, they create equal and opposite forces on each other [e.g. rocket moves forward because it pushed something else (hot gases) backward.]

Newton's Law of Universal Gravitation:
   -- all orbits are  caused by the falling inward of the planet or satellite as it simultaneously moves sideways, leading to a curved path around central mass.

 
F = G x m₁ x m_2/r2
where G = 6.67x10^-11m³/_kg._sec2
  -- several other equations fall directly from the law of gravity:
  -- one can measure a planet's or satellite's mass by using orbital motion:
M = v²r_/G
  -- surface gravity:  g = GM_/R2
  -- escape velocity:  V_esc = square root of (2GM_/R)

The following figure is the solar system as visualized after the work of Isaac Newton, and published in Newton's Principia Mathematica. It includes the orbits of all the planets visible to the naked eye in nearly circular orbits and the highly elongated elliptical orbits of many comets, including Halley's Comet named after Newton's friend, Sir Edmund Halley.  Other than the fact that three more planets, many more comets, and many asteroids have been found since then, the model we have of the solar system is almost unchanged from this image.


 

    Reasons for the Seasons

 

The 23.5° tilt of the Earth's axis with respect to the ecliptic causes the Sun to appear to move northward or southward with the yearly cycles, shining light more strongly alternately on the Earth's Northern and then Southern Hemispheres. The tilt of the Earth's axis causes two secondary effects. (1) the Sun beats more directly down in the summer than in the winter --> more direct heating. (2) the days are longer in the summer than in the winter --> more accumulated sunshine per day, and thus more accumulated heating. Both cause the summer days to be hotter than winter days. * It is summer on the northern hemisphere at the same time it is winter in the southern hemisphere, and vice versa. * One would think that the Earth's elliptical orbit would significantly affect the seasons, but itseffect is minimal. The earth is nearest the Sun (perihelion) on ~Jan. 3, and the net effect of the distance variation is to make the seasonal temperature variation slightly wider in the southern hemisphere that in the northern hemisphere.

Earth in June Earth in December * Notice that above the Arctic Circle, the Earth is continually in light in June (Summer solstice in the northern hemisphere) and continually in darkness in December (Winter solstice in the northern hemisphere). Also notice that the Seasons are exactly reversed in the southern hemisphere.

  -- approximately every seven days (one week!) the moon goes one quarter of the way through the cycle of phases.
  -- new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third (or last) quarter, waning crescent, new moon.

-- the illuminated fraction of the moon, as seen from the Earth is based on the Earth-Moon-Sun geometry (giving the phases), but the same side of the Moon always points towards the earth (with a little bit of wobble, called nutation). Given two of the three following: (1)the time of day or night, (2)the position across the arc of the sky where the Moon will appear, and (3)the phase of the Moon, you should be able to generate the third.

• eclipses and the small angle formula:

 -- as seem from the surface of the Earth, both the Moon and the Sun are the same angular size ( about 1/2 degree across), meaning they appear as big as each other.

 
L = 2pDA(degrees)_/360
    or
L = 2pDA(arcseconds)_/360x3600
where L is the actual size (width) of the object, 
D is the distance to the object, 
and A is the angular size of the object (L and D must be given in the same units, and the units of A are listed beside it.)

  umbra -- full shadow
  penumbra -- partial shadow
 
• Solar Eclipses:

  --  only happen exactly at New Moon
  --  happen when the Earth passes through moon's shadow.
  --  eclipses are only visible for observers who are themselves under the moon's shadow (the area of totality is a small patch <70km wide speeding across the Earth's surface at 1000km/hr)



 *  total solar eclipses - happen only if the angular size of moon is larger than the angular diameter of the Sun (i.e. at lunar perigee and Earth's aphelion) and the Sun/Earth/Moon alignment is perfect (exactly at Line of Nodes); useful for astronomers studying the Sun's atmosphere
 *  annular solar eclipses - happen only if the angular size of Moon is smaller than the Sun.
 *  partial solar eclipses - happen if the Sun/Earth/Moon alignment is not perfect; Earth will only pass into the Moon's penumbra.

     --------
 

• Lunar Eclipses:

  --  only happen exactly at Full Moon
  --  happen when moon passes through the Earth's shadow.
  --  visible from anywhere on the Earth in shadow (that is, anywhere that it is nighttime (and thus roughly half the world's population can see each lunar eclipse.)



     --------
 

• Line of Nodes and "eclipse seasons" 

  -- Eclipses do not happen every month because the Moon's  and Earthís orbits are tipped by ~5°; eclipses can only happen when the New or Full Moon falls near where those two orbital planes cross (i.e. along the Line of Nodes)
  -- Thus eclipses only happen for a short period (of about a month's duration, called an "eclipse season") twice each year. The time during the year when this happens changes because of an 18.3-year wobble in the planes of the orbits called the Saros cycle.)

  -- The variation of the Moon's gravity across the Earth is an example of a  differential or tidal force. 
  -- Deforms Earth' s oceans into a prolate spheroid.  The residual differential force causes two high tides per day and two low tides. 
  -- Rocks move a few cm; ocean move more than 1 meter [and depending on the geometry of the coastline, which focuses the motion of the water, by up to 7-8 meters (eg. Bay of Fundy, Canada).]
  -- spring tides and neap tides: effects of tides from the Moon and Sun either add or subtract.

* highest high tides and lowest low tides are at new and full moon (spring tides).
* weaker range of tides at first and third quarter moon (neap tides).
(should be able to also figure out what times of day each high or low tidewould happen).

  -- effects of tides are seen everywhere, not just on Earth; [e.g. Moon's locked rotation, Io's volcanoes, rings of Saturn, binary stars, etc.]

• Electromagnetic Radiation:

  -- all electromagnetic radiation (composed of oscillating electric and magnetic fields) always travels a single speed through space, called the speed of light:
        c = 3 x10⁵km_/sec
  -- the longer the wavelength, the lower the energy of the associated wavepacket (photon), and the shorter the wavelength, the higher the energy:
        E = hc_/l
  -- gamma rays (g), x-rays, ultraviolet, visible light, infrared, (microwave), radio waves. [from shortest wavelength to longest wavelength (highest energy to lowest energy).]
  -- visible light wavelengths ~400nm - 700nm (4000Å -7000Å)
  -- infrared radiation is what we sense as heat.
  -- other than wavelength (which affects energy), all electromagnetic radiation is really pretty much 'the same thing'.
 
• Interaction of Light and the Atmosphere:

* Opacity (and Transparency) of the Atmosphere:
   -- visible light range and radio waves (and a small amount of the infrared and ultraviolet spectra) are the only parts of the entire EM spectra that the Earth's atmosphere is transparent to.
    -- the atmosphere blocks or absorbs (is opaque to) rest of the EM spectrum.
    -- x-rays and g-rays are blocked by oxygen and nitrogen in upper atmosphere.
    -- UV blocked by ozone in the upper atmosphere; protects us from skin cancer, and all life from continuous mutation.
    -- water vapor and carbon dioxide in lower atmosphere absorb most IR; causes our lower atmosphere to be warmer than normal -- Greenhouse effect.
    -- telescopes for visible and radio wavelengths can be on the Earth's surface, but all others must be carried on satellites.

* Refraction and Dispersion of Light in the Atmosphere:
    -- caused by small particles and molecules in the atmosphere. More particles = more scattering (dispersion).
    -- if there were no atmosphere, the sky in daylight would be black.
    -- stronger scattering of shorter wavelengths of light causes the sky to look blue.
    -- weaker scattering of longer wavelengths of light causes sunsets to be brilliant orange-red.

* Twinkling of Stars: (astronomers call it "seeing")
    -- caused by turbulence and pockets of warmer and cooler air moving across the line of sight to the stars, as the air pockets are moved by wind currents.
 

• Temperature:

  -- temperature is a way to measure of the motion and energy of atoms.
  -- the greater the internal energy of the matter, the more the atoms vibrate or bounce off each other , and the higher the temperature.
  -- the states of matter with increasing temperature: solid (at zero temperature -- frozen -- all atomic motion stopped), liquid, gas, molecules break apart (atoms, free radicals), ions (electrons strip off atoms), at highest temperature many electrons strip off of each atom (multiply ionized).
  -- Kelvin Temperature scale only scale that starts at true (absolute) zero where all motion stops. (273K -- freezing point of water; 373K -- boiling point of water; 300K average room temperature)

* Weins Law:
  -- All matter gives off radiation over a broad wavelength range associated with its temperature, called blackbody radiation or continuum spectra.

  -- the greatest amount of energy (the maximum intensity) is given off at a particular wavelength associated with the emitting object's temperature by:

T(K) = 3,000,000_/lmax(nm)
      or
lmax(nm) = 3,000,000_/T(K)
 

* Stefan-Boltzmann Law:
  -- The total amount of light a star (or any other warm or hot object) gives off, its Luminosity, L, is related its size -- specifically its surface area 2pR² -- and also to the objects temperature.
 
L = 2pR^{2 .}sT⁴
  -- where s is called Boltzmann's constant 
       s = 5.67 x 10^-8 W/m^2.k⁴


  -- blue stars are hotter that white stars, which are hotter than red stars.
  -- hotter stars are brighter than cooler stars, and the brightness goes up very fast, as the fourth power of the temperature.
  -- larger stars are brighter than small stars.
 

• Interaction of Light and Atoms:

  -- atoms have discrete energy levels like stair steps; the electrons in each atom can only have those precise energies, and not in between. 
  -- the energy levels of each atom depend on how many electrons the atom has; and thus each different element, (and each different ionization state for each element) has a unique set of energy spacings -- a "fingerprint" that can be used to identify the element and state.

  -- Absorption: atoms absorb light (and create a dark band at one wavelength or color) when some of the incident light wavelengths match the precise energy of available transitions in the atom  -- the electrons hop from lower energy states to higher energy states.
  -- Emission: atoms emit light (and create a bright line at one wavelength or color) if they have electrons that have previously been excited up to higher energy states -- the electrons will drop from the higher energy state to lower energy
  -- in both of these processes, the light's energy (and thus wavelength) is defined by the energy differences between the energy levels in that atom.
 

• Three Types of Spectra:

  -- continuum spectra: from hot opaque sources (Can obtain the sources temperature.)
   -- absorption spectra: from cool or warm gas cloud between observer and hot source (Can find the elements present in the cloud -- dark bands on continuum spectrum).
  -- emission spectra: from warm or hot gas cloud observed directly (Can find the elements present -- bright bands).

Doppler Effect:

  -- used to measure the relative motion of the source and observer.
  -- works for all waves: water, sound electromagnetic radiation (light).
  -- seen in stellar spectra as a small shift in the (wavelength) positions of absorption or emission lines.
  -- a shift to shorter wavelength (blueshift) means they are approaching, and shift to longer wavelengths (redshift) means receding or separating.

Dl = l - l_o = l_ov_r/c
       or
v_r = c^.Dl_/l = c^.(l - l_o)_/l
where Dl is the wavelength shift, 
l_o is the original wavelength (measured from an unmoving source),
l is the wavelength of the moving source,
v_r is the speed of the source radially toward or way from the observer (*movement laterally across the line-of-sight is unobservable)
and c is the speed of the waves (usually the speed of light)

Astronomical Tools:

• Refraction and Reflection of Light

-- Refraction depends on the bending of light as it passes through a transparent medium.

  * the precise shape ("figure") of both surfaces are important.
  * the density, uniformity, transparency, and composition of the lens is critical.
  * refractive telescopes suffer from chromatic aberration (because different wavelengths focus at different lengths.)
  * glass sags under its own weight, and also thermally deforms under temperature changes (normally this is undetectable, but because of the unbelievably precise requirements of telescope optics, this sagging distorts and degrades the telescope images. (especially true of very large refracting telescopes because the glass is very heavy and they can only be supported around the perimeter of their objective lenses.) 

  * the largest refracting telescope is 1.04-meter telescope at Yerkes Observatory, Wisconsin)

  -- Reflection depends on the precise angles between incoming and outgoing reflected light rays.

  * the "figure" or shape of only one surface, the front surface is important -- easier to make very large telescope optics.

  * the largest refracting telescopes are the 10.0-meter diameter Keck-I and Keck-II, each composed of 36 segmented mirrors on Mauna Kea, Hawaii.  (Advances in very large telescope design have allowed the building of several very large optical telescopes, with the following, all over 8.0-meters being commissioned in the last few years:
  * Gemini-North (Mauna Kea) and Gemini-South (Cerro Pachon, Chile) -- each 8.0 meters
  * Subaru (Mauna Kea) -- 8.3-meters
  * Very Large Telescope (VLT) (Cerro Paronal, Chile -- European Southern Observatory) -- four x 8.0-meter, on same mountain peak, that can be coupled together (interferometry), or used separately.
  * Hobby-Eberly (Ft. Davis, Texas) -- 9.4-meter (spherical)

• Three Powers of a Telescope:

  -- the ability to detect very faint objects:
Light Gathering Power
 
LGP_A = D_A²
LGP_B   D_B²
  * the amount of light that a telescope can gather (effectively how faint the dimmest object that can be observed) is related to the surface area of the input aperture or objective -- pR² or pD²_/4
  * the larger the objective diameter, the more light that can be gathered.
  * improved by long time-exposures  (max. time human eye can integrate light ~1/30 sec.)
  * also improved by advances in photographic film.
  * more recent advances by using long time-exposures with very sensitive electronic sensors: CCD's.
  * biggest problem is "light pollution" - can't see anything dimmer than the overall glow of the sky which is caused by upward scattered light from cities.


-- the ability to separate the images of two objects very close together:

Resolution:
  -- the smallest angle between two bright point sources whose images can be visually distinguished.
  -- the smaller the resolution angle, the better!!
      several things limit telescope resolution:
       1. Diffraction: the intrinsic limitation due to the passage of the light through 
an entrance aperture of finite size.
   * this limit (called the Dawe's limit or resolution limit) is dependent on the diameter of the telescope's input (or objective) lens or primary mirror.
   * forces the image to be smeared out into rings around each bright  spot on an image.
   * the larger the telescope objective, the smaller the angular separation that can be resolved.
 
for visible wavelengths, the minimum resolved angle is:
a(arcsec) = 11.6_/D(cm)
for all wavelengths (resolution is dependent both on aperture and wavelength, with long wavelengths like radiowaves requiring huge apertures to get good resolution.) the minimum resolved angle is:
a(arcsec) = 2.0x10^-3.l(Å)_/D(cm)
       2.  Any imperfections in the telescope "figure".
   * the most common is 'spherical aberration', where the mirror is not polished to ideal shape (a parabola), but distorted to be more spherical in shape.
   * also roughness, poor alignment of the telescopes optical components, jitter in the mounting of the telescope as it track stars, etc.
       3.  Limitations due to passage of light through the atmosphere:
   * often, for the largest telescopes, the resolution is not limited by diffraction, but by "seeing", the twinkling caused by heat, wind currents, turbulence, and density variations in the atmosphere.
 
for visible wavelengths, the minimum resolved angle is:
a(arcsec) = ~2.0     (observer at sea-level)
a(arcsec) = ~0.5     (observer on highest mountain peak)
    * this last limitation is very recently being reduced using a technique called "active" or "adaptive" optics, where, using super-computer control, the shape of one of the mirrors in the telescope is continually adjusted by hundreds of tiny actuators to compensate for variations in the arrival time of different parts of the image wavefront due to "seeing".
-- the ability to multiply or visibly expand the size of images:
Magnification:

   * this is, by far, the easiest of the powers of a telescope to obtain or to change, because although the objective optics (lens or mirror) is fixed, the very small eyepiece lenses are easily interchangeable.
   * sometimes magnification is good, and sometimes it doesn't help (as in when the object being observed covers a large angular patch of the sky.)
   * magnification does not depend on the diameters of the optical elements, but rather on their focal length (effectively how strongly the lenses or mirrors are curved):
 

M = fo_/fe
where fo is the focal length of the objective lens (mirror),
and fe is the focal length of the eyepiece lens.

Satellite Astronomy