Astronomy 1143 Final Exam Review Answers
Prof. Pradhan
April 24, 2015
What is Science?
1. Explain the difference between astronomy and astrology.
• Astrology: nonscience using zodiac sign to predict the future/personality traits.
• Astronomy: scientific study of planets, stars, galaxies, and the universe.
2. What number is the metric system based around? What are some of the more widely-used prefixes?
• 10
• milli-: 1/1000th, centi-: 1/100th, kilo-: 1000
3. What special attribute of certain constellations puts them in the zodiac?
• They lie in the plane of the Sun’s orbit around the Earth (the ecliptic plane).
Observational Astronomy: The Night Sky
1. What is the ecliptic plane?
• The plane of the Sun’s orbit projected on the sky. Since all the planets have low inclination, it is
also where they lie, as well as the zodiac.
2. Why is the ecliptic tilted with respect to the celestial equator? How big is this tilt in degrees?
• Because the Earth’s rotation is tilted with respect to its revolution around the Sun.
• 23.5 degrees.
3. Where does the ecliptic plane intersect the celestial equator?
• The Vernal Equinox (0 degrees right ascension, 0 degrees declination)
4. What are the primary coordinates for finding a place on Earth? How about the celestial sphere?
• Earth: longitude and latitude.
• Celestial sphere: right ascension and declination.
5. In what constellation would you find Polaris?
• Ursa Minor.
6. What is the angular size of an object? What is it for the Moon?
• It is the angle subtended in your field of view by the object.
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• The moon is about 30’ in the sky.
7. How big is an arcminute? An arcsecond?
• 1’ = 1/60th of a degree.
• 1” = 1/60th of an arcminute = 1/3600th of a degree.
8. What is stellar parallax? Why is it useful?
• Stellar parallax is the apparent change in position of stars brought about by the motion of the
Earth around the Sun.
• It can be used to determine the absolute distance to stars.
9. Why couldn’t the ancient Greeks see parallax, and what did they think this meant?
• Even for the nearest star, the parallax is far too small to see with the naked eye.
• They took this to mean that the Earth didn’t move.
10. What is a parsec? How many light years are in a parsec?
• A parsec is the distance an object must have from Earth to have a parallax of 1” = 1 arcsecond.
• 1 pc = 3.26 ly
The Heliocentric Model
1. In simple terms, what are the geocentric and heliocentric models?
• Geocentric: the planets and Sun all orbit around the Earth.
• Heliocentric: the planets, Earth included, all orbit around the Sun.
2. Who was the first major proponent of the heliocentric model? What were the key facets of his model?
• Copernicus.
• His model had a central Sun with the planets orbiting it. This would explain why the Sun is
always seen on the ecliptic.
• It also included epicycles, like Ptolemys geocentric model, to preserve circular motion.
3. Explain the main observational problem that Mars presented for the Geocentric and early Heliocentric
models.
• Retrograde motion: Mars would abruptly change its direction of motion on the sky and then flip
back periodically.
4. What did Ptolemy add to the geocentric model explain this problem?
• By adding epicycles, i.e. circular orbits within circular orbits, to the planets’ motion around the
Earth.
5. Who correctly solved this problem? How? Using whose data?
• Johannes Kepler solved this by incorporating elliptical orbits rather than perfectly circular ones,
compiled from Tycho Brahe’s data.
6. Which of Galileo’s observations supported the heliocentric model?
• Phases of Venus.
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• Satellites of Jupiter (something else in the solar system has objects orbiting it besides the Earth).
7. What else did Galileo discover with the telescope?
• Mountains and craters on the surface of the Moon
• The Milky Way is actually made up of individual stars even though they all blend together when
you look without a telescope
8. Define: superior planet, inferior planet, conjunction, opposition, quadrature, perihelion, aphelion, and
eccentricity.
• Superior planet: one whose orbit around the Sun is outside that of the Earth’s.
• Inferior planet: one whose orbit around the Sun is internal to that of Earth’s.
• Conjunction: occurs when the Sun is directly between the Earth and a superior planet, an inferior
planet is between the Earth and the Sun (inferior conjunction) or the Sun is between an inferior
planet and the Earth (superior conjunction).
• Opposition: occurs when the Earth is directly between the Sun and a superior planet.
• Quadrature: occurs when the Sun and a superior planet are 90 degrees apart.
• Perihelion: the closest a body comes to the Sun in its orbit.
• Aphelion: the farthest a body gets from the Sun in its orbit.
• Eccentricity: a measure of how much a 1 sided object deviates from being a perfect circle. Is 0
for a circle, 1 for a straight line, and determined by the ratio of semiminor to semimajor axis.
9. Venus is on the opposite side of the Sun compared to the Earth. What is the name for this configuration
of an inferior planet?
• Superior conjunction.
10. What is a synodic period of a planet? Sidereal period?
• Synodic period: time it takes for a planet to return to the same spot on the night sky. Similar to
“solar day”.
• Sidereal period: time it takes for a planet to return to the same spot in its orbit around the Sun
with respect to a fixed observer (the stars).
11. Are planetary orbits perfectly circular as proposed by Kepler?
• No, they are on elliptical orbits.
12. Explain Kepler’s 3 Laws.
• 1st Law: All the planets are on elliptical orbits, with the Sun at one of the focii.
• 2nd Law: In their orbits around the Sun, every planet sweeps out equal area in equal time.
• 3rd Law: The square of the period of any orbit is proportional to the semimajor axis of said orbit
to the third power.
13. What is the proportionality between period and semimajor axis in Kepler’s 3rd Law?
• Period squared is proportional to the semimajor axis cubed.
14. Whose observations did Kepler use in order to come up with his laws of planetary motion?
• Tycho Brache’s
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Forces, Accelerations, and Laws of Motion
1. What are Newton’s Three Laws of Motion?
• An object in motion will stay in motion if there are no outside forces acting upon it (like friction),
and an object at rest will stay at rest unless outside forces act on it (like pushing or pulling, or
gravity).
• F = ma, which means that the force on an object of mass m will give it an acceleration a through
this relation
• Every action has an equal and opposite reaction. For example, if you push on a wall, it pushes
back at you just as much. A star feels just as much gravitational force from a planet as the planet
does from the star (but the star has a far bigger mass so it will experience far less acceleration).
2. What is inertia?
• Inertia is an object’s resistance to changes in its motion. An object with high inertia requires a
lot of force to get moving if it’s still and a lot of force to get it to stop if it’s moving.
• The amount of mass that an object has determines how much inertia it has.
3. What is the equation that governs the gravitational attraction between two bodies?
• F = Gmr12m2 , where G is Newton’s gravitational constant, m1 and m2 are the masses of the two
objects, and r is the distance between them.
4. Explain Kepler’s 3 Laws.
• 1st Law: All the planets are on elliptical orbits, with the Sun at one of the focii.
• 2nd Law (Law of Equal Areas): In their orbits around the Sun, every planet sweeps out equal
area in equal time.
• 3rd Law (Harmonic Law): The square of the period of any orbit is proportional to the semimajor
axis of said orbit to the third power. Note: This is true for both circular and elliptical orbits.
5. What is the proportionality between period and semimajor axis in Kepler’s 3rd Law?
• Period squared is proportional to the semimajor axis cubed.
• If the units of period are years and the units of semimajor axis are AU, then period squared is
exactly equal to semimajor axis cubed.
6. Why do things with mass feel heavy here on Earth?
• Gravity is pulling them toward the Earth, so you must exert a force on them to hold them up.
7. Is weight, or how heavy something feels, a force or a mass?
• Weight is a force. Without the acceleration of gravity pulling on an object, it would have no
weight.
• Mass is just a measure of how much inertia an object has, not how much it weighs.
8. What determines how fast an object falls toward the Earth when dropped?
• The strength of gravity of the Earth, and the air resistance on the object. If air resistance is
neglected, all objects fall at the same speed and the same acceleration NO MATTER THEIR
MASS.
9. What is the gravitational acceleration of the Earth, g, and who first measured it?
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• g = 9.8 m/s2
• Galileo
10. What are the units for force, mass, and acceleration?
• Force: Newtons, or kilogram-meter per second squared.
• Mass: kilograms or grams.
• Acceleration: meters per second squared, which is equivalent to saying meters per second per
second.
Light
1. What is light?
• Light is electromagnetic energy that travels through space at a speed c
• It is both a particle (photon) and a wave
2. How is light created and what can light interact with?
• Light is created by moving electric charges, like electrons
• Light can only interact with particles that have an electric charge, like electrons
3. How is the wavelength of light related to its frequency?
• c = λf , where c is the speed of light (c = 300, 000, 000 m/s), λ is the wavelength, and f is the
frequency
4. What are the units for frequency and wavelength?
• Frequency is measured in hertz (Hz), which are inverse seconds 1/s
• Wavelength is measured in many units of distance depending on how big it is, from angstroms
(Å, 1 Å = 10−10 m) to nanometers (nm, 1 nm = 10−9 m) to millimeters, centimeters, or even
meters or kilometers for very long waves. Mostly we’re interested in light with wavelengths the
size of a few thousand angstroms, like visible light.
5. List the electromagnetic spectrum from highest energy to lowest energy. Note that this is also the list
from shortest wavelength to longest wavelength, and the list from highest frequency to lowest frequency.
• Gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves
6. Do different wavelengths of light travel at different speeds in the same medium?
• Absolutely not! All light, everything from radio to gamma rays, travels at the speed of light.
• All light travels at the speed of light, and nothing but light can travel at the speed of light.
7. What wavelength range is visible light?
• 4000 Å(blue) to 7000 Å(red) is visible, but the human eye is most sensitive in the somewhat
reduced range of 5000 Åto 6000 Å
8. List the visible colors in order of increasing frequency (increasing energy and decreasing wavelength).
• red, orange, yellow, green, blue, indigo, violet (ROYGBIV)
9. How does the energy of a photon relate to other properties of light?
• E = hf = hc/λ, where E is the energy of a photon, f is its frequency, λ is its wavelength, c is
the speed of light, and h is Planck’s constant
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Atoms and Spectroscopy
1. What subatomic particles make up the atom?
• Positively charged protons and neutrally charged neutrons in the nucleus, negatively charged
electrons in “orbits” around them
2. Which subatomic particle is most important for determining which element an atom is?
• The proton. An element is defined entirely by how many protons it has.
• Different numbers of neutrons make up different isotopes of the same element, but it’s still the
same element.
• The number of electrons determines the overall charge of an atom, but you can remove an electron
(ionize the atom) and it’ll still be the same element.
3. How many protons, electrons, and neutrons does a hydrogen atom have?
• One proton and one electron, no neutrons. A neutral atom (an atom without any charge) always
has equal numbers of protons and electrons.
4. Can electrons be anywhere around the nucleus?
• No. Electrons must be in specific orbits around the nucleus with specific amounts of energy.
5. What happens when an atom emits light? What is the energy of that light?
• An atom can emit light when one of its electrons is in a large, high-energy orbit around the
nucleus, and then the electron moves to a smaller, lower-energy orbit. The energy of the photon
that is emitted is equal to the energy difference between the two orbits that the electron moved
between.
6. What happens when an atom absorbs light? Can an atom absorb light of any energy?
• An atom can absorb light by moving one of the electrons to a higher-energy orbit than it was
originally in. The energy difference between the two electron orbits must be equal to the energy of
the light, so an atom can’t absorb every energy of light. It can only absorb light with the correct
energy that matches the energy difference between electron orbits.
7. What does an emission spectrum look like, in general, for a single element?
• An emission spectrum will be mostly dark with bright emission lines at the specific energies where
the atom can emit light. These energies are equal to energy differences between different electron
orbits in the atom.
8. What does an absorption spectrum look like, in general, for a single element?
• An absorption spectrum is mostly bright, with dark absorption lines where light is missing at
the specific energies where the atom can absorb light. These energies are equal to the energy
differences between different electron orbits in the atom.
9. What are some of the most well-known emission and absorption series of lines of hydrogen, and what
part of the electromagnetic spectrum are they in?
• The Lyman series: the electron transitions from higher-energy orbits to the lowest-energy orbit,
seen in ultraviolet light
• The Balmer series: the electron transitions from higher-energy orbits to the second lowest-energy
orbit, seen in visible light
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• The Paschen series: the electron transitions from higher-energy orbits to the third lowest-energy
orbit, seen in infrared light
10. What can you learn from looking at the spectrum of a star?
• You can learn its temperature based on the wavelength where it emits the most energy
• You can learn what elements make up its photosphere based on the absorption lines present, since
each element has its own distinct pattern of emission and absorption
• You can learn how fast it’s moving toward or away from us (Doppler effect: see section below)
11. What is a blackbody?
• A blackbody is a perfect absorber and emitter of radiation. It emits exactly as much radiation as
it absorbs, and this causes it to have a certain temperature.
12. What is temperature?
• Temperature is the random motions of atoms or molecules. Higher temperature means more
motion, lower temperature is less motion.
13. What is absolute zero?
• It is the lowest temperature anything can have, where all random motions completely stop.
Doppler Effect
1. What causes the Doppler effect?
• Wavelengths get “squished” when the object emitting them is moving toward you, because the
object starts to “catch up” with the wave while it continues to emit
• Wavelengths get “stretched” when the object emitting them is moving away from you, because
the object is moving away from the wave while it continues to emit
2. What kinds of waves exhibit the Doppler effect?
• All kinds! We observe the Doppler effect in light and sound. In everyday life, it’s much easier to
observe in sound (think police car siren zooming by you) because sound travels MUCH slower than
light. This makes it easier for the object to “catch up” or “leave behind” its sound wave. Objects
moving very fast, like stars, have detectable Doppler shifts in the light they emit. Technically
even slow-moving objects, like a person walking toward or away from you, exhibit Doppler shifts
in the light coming from them, but it’s such a small change because walking speed is such a small
fraction of the speed of light that you can’t detect it with your eye.
3. If a star has an emission line at a particular wavelength λ, will the observed wavelength be longer or
shorter if the star moving away from us? What color will this emission line be shifted toward?
• The wavelength of the star’s emitted light will be longer if it’s moving away from us. Since red
light has longer wavelengths than blue light, this light is shifted toward red, and we say that it is
“redshifted.”
• If the star was moving toward us, the light would be “blueshifted.”
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Relativity
1. What are the two postulates of relativity?
• Light travels at the same speed for all observers, no matter how fast those observers are traveling,
and this speed is the maximum speed anything can move
• All physical laws must be the same everywhere
2. How is the energy of an object related to its mass?
• E = mc2 where E is the energy, m is the mass, and c is the speed of light
3. Why can’t objects move at the speed of light?
• It would require infinite energy to accelerate them up to that speed.
4. What is the important idea in general relativity?
• Gravity is just acceleration! If you’re traveling on an accelerating vehicle, it feels the same as
gravity.
5. What are time dilation and space contraction?
• Time dilation: Time moves slower for moving observers than for those who are stationary
• Space contraction: Objects appear shorter for moving observers than for those who are stationary
Telescopes
1. Why do we use telescopes?
• The apparent brightness of distant objects decreases with the square of the distance to them, so
distant objects are extremely faint.
• If we can build something that stares at something for a long time and can collect as much light
as possible from that thing, then maybe we can see it.
2. What is the difference between a refracting and a reflecting telescope?
• Refracting: light is bent and focused by passing through glass lenses.
• Reflecting: light is bent and focused by bouncing off of mirrors.
3. What happens when light passes through a lens?
• Light travels slower in glass than in air, so the path of light gets bent at the interface between
glass and air.
• Red light doesn’t get bent as much as blue light, so there can be chromatic aberrations where
the image separates into a red image and blue image.
• This “bending” of light by altering its speed is used to focus a wide area of light down to a
pinpoint.
4. Where is the best place to put a telescope?
• Space! Then we don’t have to deal with the Earth’s atmosphere, which absorbs mostly UV light.
• If we can’t put a telescope in space, then any place where the atmosphere doesn’t cause as many
problems: dry, high, dark places.
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5. How does the power of a telescope scale with its diameter?
• Power = π(D/2)2 , where D is the diameter. So doubling the diameter will quadruple (22 = 4)
the power.
6. What is the purpose of a telescope’s eyepiece?
• To magnify the focused image. The telescope itself does not magnify anything.
7. List a few of the important telescopes in use today.
• Keck: Largest optical telescope with a 10 meter diameter, in Hawaii.
• Large Binocular Telescope (LBT): Owned by OSU, has two 8 meter mirrors, in Arizona.
• Hubble Space Telescope (HST): 2.4 meter, but huge advantage because it’s in space and doesn’t
have to see through the atmosphere.
• Arecibo: In Puerto Rico, 1000 foot radio telescope.
Stars
1. What is a star?
• A ball of gas with temperatures high enough at the center for hydrogen to be converted into
helium via nuclear fusion, which converts mass into energy
2. What is the H-R Diagram?
• The Hertzsprung-Russell Diagram is a plot of stars’ luminosity (brightness) vs. temperature. Stars
with higher temperatures have higher luminosities. Note that the temperature axis is reversed:
higher temperature is on the left, lower temperature on the right (but higher luminosity is still
toward the top and lower toward the bottom).
3. How are the luminosity, radius, and temperature of a star related?
• L = 4πσR2 T 4 , where L is luminosity, R, is radius, and T is temperature. σ is the StefanBoltzmann constant
4. What other properties of a star increase when the star’s mass increases?
• Luminosity, temperature, and size
5. What determines the color of a star?
• Its temperature: hotter stars are bluer and colder stars are redder
6. How do we classify stars?
• Using the spectrum of a star, we can determine its temperature and color, and stars are organized
in this way. Stellar types from hottest to coolest are: O, B, A, F, G, K, M, L
7. Which layer of a star is the part that we see?
• The photosphere. This is easy to remember because it’s almost has “photon” right there in the
name.
8. What is a globular cluster?
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• A globular cluster is a group of stars held together by mutual gravitational attraction between
the stars.
• The types of stars that make up globular clusters are old, because there is not ongoing star
formation in globular clusters to produce new, young stars.
• Since the stars are old, they also tend to be metal-poor, meaning that they only have hydrogen
and helium. This is because metals are created in stars and if these stars were formed too early
in the universe for there to have been many stars around making metals, then there just wouldn’t
have been enough metals that went into the stars when they formed.
Hertzsprung-Russell Diagram and Luminosity Relations
Figure 1: The Hertzsprung-Russell diagram. Note that temperature increases to the left. The line through
the middle is the main sequence, the lower line is the white dwarf sequence, and the lines in the upper right
are the red giant and supergiant sequences (supergiant is on top).
1. What does a star’s location on the HR diagram tell us?
• Its abolute magnitude, from which you can get its luminosity, and its spectral color, from which
you can get its temperature. Indirectly, you can also get its mass by how far up or down it is on
the main sequence, if it is on the main sequence.
2. What is the main sequence?
• The sequence on the HR diagram of the main hydrogen-burning phase of a star’s life. More
massive stars are up and to the left, less massive stars down and to the right.
3. Where is the red giant sequence on the HR diagram? What does this location mean?
• It is up and to the right of the main sequence.
• Red giants on this sequence are cooler and more luminous than stars on the main sequence.
4. What is the most important stellar property that determines all other properties of a star?
• Its mass!
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5. How does a star’s radius and temperature relate to its luminosity?
• L = 4πR2 σT 4 , where R is the radius, T is the temperature, and σ is the Stefan-Boltzmann
constant.
6. How does a star’s aparent brightness relate to its luminosity?
• F = L/(4πd2 ) where F is the flux, or relative brightness, L is the luminosity, and d is the distance
to the star.
Spectral Types of Stars
1. What is the spectral sequence of stars, from hottest to coolest?
• O, B, A, F, G, K, M, L (Helpful mnemonic: “Oh, Be A Fine Girl, Kiss Me Lovingly”)
2. What color are hot stars? Cool stars?
• Hot stars are bluer.
• Cool stars are redder.
3. What causes stars to have a specific color?
• A star’s color is just the wavelength at which its emission is strongest, the peak of its spectral
distribution.
4. Do O and B type stars show hydrogen lines in their atmospheres?
• No, they do not. Even though they, like all stars, are made up mostly of hydrogen, they’re so hot
that hydrogen is ionized and thus doesn’t absorb light from the star in spectral lines.
5. What spectral type is the Sun? What is the Sun’s effective temperature?
• The Sun is a G star.
• The Sun has a temperature of 5800 K.
6. What part of the spectrum does most of the Sun’s light come out in?
• Visible
Life of Low Mass Stars
1. What is the mass cutoff for a “low mass” star?
• Low mass stars are any stars with a mass less than 3 times the mass of the Sun, so the Sun is
considered a low mass star.
2. How does a low mass star spend most of its life?
• Fusing hydrogen into helium in its core, staying on the main sequence.
3. What happens when a low mass star stops fusing hydrogen?
• It moves off the main sequence and swells up into a red giant. It moves into the red giant branch
of the HR diagram, then the asymptotic giant branch (AGB).
• The outer shells of the star get thrown off and create a planetary nebula.
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• The core that is left behind becomes a white dwarf.
4. What is the maximum mass that a white dwarf can have? What is this mass called? What happens
if this mass is exceeded?
• 1.4 times the mass of the Sun.
• This is called the Chandrasekhar limit.
• If the Chandrasekhar limit is exceeded, the white dwarf collapses under its own weight into a
neutron star or, if the mass is exceeded by enough, a black hole. This means that white dwarfs
absolutely can not be more massive than 1.4 Solar masses!
5. What is a white dwarf?
• A white dwarf is the core of a low-mass star that is left behind after the star dies.
• It is made up of either helium or carbon and oxygen.
• It is supported against its own gravitational collapse by electron degeneracy pressure.
6. What is the largest element a low mass star can fuse in its core?
• Carbon or oxygen.
Life of High Mass Stars
1. What happens to a high mass star after the main sequence?
• It’s done fusing hydrogen in its core.
• It begins fusing other elements in the core, from helium through carbon, oxygen, neon, magnesium,
silicon, etc. all the way up to iron.
• It enters the supergiant branch of the HR diagram.
• When it can no longer fuse elements in the core (once it gets to iron), it explodes as a supernova.
• It leaves behind either a neutron star or a black hole.
2. What is a neutron star?
• The core of a dead massive star that is so dense that no elements exist in it, just neutrons.
• It is supported by neutron degeneracy pressure.
Supernovae
1. How massive does a star have to be in order to end its life in a supernova?
• Stars with masses more than about 8 times the mass of the sun will undergo core collapse and be
seen as a supernova.
2. What causes a core-collapse supernova?
• Very massive stars fuse elements in their core all the way up to iron. But iron fusion requires
energy instead of releasing energy, so when the core reaches the point where it is made of iron,
it can no longer fuse and therefore cannot support its own weight. This causes the iron core to
collapse, which then violently throws off the outer layers of the star in a supernova explosion.
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Our Universe
1. Is the universe expanding, contracting, or staying the same? How do we know this?
• The universe is expanding. We know this because the further away an object is from us, the
redder it appears to be. Because of the Doppler Effect, we know this means it must be moving
away from us, and objects further from us are moving away faster.
2. What do we mean when we say the universe is “expanding?”
• Space between objects like galaxies is expanding, pushing the galaxies apart from each other. The
galaxies themselves are not moving apart, it’s just space getting bigger between them.
3. If everything in the universe is expanding away from us, does this mean we’re at the center of the
expansion?
• Nope! Think about an expanding loaf of bread with raisins in it. We could be sitting on a raisin
near the edge of the loaf, but still all the other raisins we could see would be moving away from
us.
• Also, the raisins themselves (analogous to galaxies) aren’t expanding. They’re just moving away
from each other.
4. What is Hubble’s Law?
• v = H0 d, where v is the velocity of a galaxy (which we can determine from the redshift), d is the
distance to that galaxy, and H0 is Hubble’s constant.
5. Using Hubble’s law, how can we determine the age of the universe?
• Since the universe is expanding and must have had a beginning, then 1/H0 is the time it took for
galaxies to get where they are now.
6. Using Hubble’s constant, how can we determine the size of the observable universe?
• Since the universe has a finite age, we can multiply this by the speed of light to determine how
far light could travel during the age of the universe, and this is the farthest we could see.
• The age of the universe according to the Hubble Law is 1/H0 , so the maximum distance we could
see is c/H0 , where c is the speed of light.
7. What is the important caveat to using Hubble’s Law and Constant to determine the age and size of
the universe?
• Hubble’s Law assumes a constant expansion rate for the universe, which means that gravity and
dark energy couldn’t be affecting the expansion rate.
• Therefore, the answers to the two previous questions are only true for a universe in which there
is no gravity and no dark energy.
8. What is the Cosmic Microwave Background?
• The CMB is radiation left over from the Big Bang. It’s a blackbody with a uniform temperature
of 2.73 Kelvin pretty much everywhere, except it has some small variations due to the presence
of matter right after the Big Bang.
9. How do we know there’s dark matter?
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• Stars rotate about galaxies with a speed determined by the mass of the galaxy and how far those
stars are from the galaxy’s center. This speed should decrease with distance, but we see that it
doesn’t. Therefore, there must be more mass in galaxies than we can see, so there must be dark
matter.
10. What are the most abundant elements in the universe?
• Hydrogen and helium
11. What does a flat rotation curve of galaxies tell us?
• Flat rotation curve means that galaxies have matter distributions that are roughly spherical, but
we only see stars in a disk. Therefore, there must be dark matter making up the sphere.
12. What is Olbers’ Paradox? What is the resolution?
• If the universe is infinitely old and big, then the entire sky should be filled with stars.
• It’s not, so either the universe isn’t infinitely old or isn’t infinitely big.
• The resolution is that the universe is not infinitely old. It began about 14 billion years ago with
the Big Bang.
13. What is the 21-cm line and why is it useful for cosmology?
• This is a spectral line of hydrogen that occurs when the hydrogen’s electron spontaneously changes
its spin from up to down.
• It is useful for cosmology because all hydrogen emit this line, so we can use it to map where
hydrogen is in the universe. Since hydrogen will cluster with other matter (like dark matter), we
can then use it to figure out where dark matter is.
Cosmological Distance Ladder
1. What is the Distance Ladder?
• It is the list of methods of measuring distances to objects. Each method only works for a range
of distances, so multiple methods are needed to obtain the full range of distances that we see in
the universe.
2. On what is each step of the Distance Ladder calibrated?
• Each step is calibrated on the slight overlap it has with the previous step. This is called a
“bootstrap” method.
3. List the “rungs,” or methods, of the Distance Ladder by increasing distance.
• Trigonometric parallax (works up to 1000 parsecs): Nearby objects (outside the Solar System)
change position relative to background stars as the Earth moves around the Sun over the course
of the year. d = 1/p where p is the angular change in relative position of the object in arcseconds
and d is its distance in parsecs.
• Spectroscopic parallax (works up to 50−60 kiloparsecs): Measure the spectral type and brightness
of a star, use the Hertzsprung-Russell diagram to figure out what luminosity a star of that spectral
type must have. Since brightness of a star depends on luminosity and distance to the star, can
use the measured brightness and the HR-diagram luminosity to find the distance (brightness =
luminosity / (4π× distance2 )).
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• Cepheids and RR Lyrae (works up to 30 − 40 Megaparsecs): These types of stars pulsate with a
regular period that’s easily measurable. The luminosity of these stars is correlated with the period
of pulsations, so if you know the period and can measure the brightness, can find the distance
through the luminosity-brightness-distance relation (brightness = luminosity / (4π× distance2 )).
This method requires a calibration to get the overall magnitude of the luminosity-period relation,
so need another distance-measuring method to calibrate this one before it can be used.
• Tully-Fisher relation (works as far as you can measure rotation curves of galaxies): The total
mass of a galaxy (including dark matter) gives the galaxy some rotation speed, which is just how
fast it’s spinning. But the total mass is also related to the total luminosity of the galaxy, because
galaxies with more stars have more mass and also emit more light. So even though we can’t
directly measure the total mass of the galaxy (since most of it is dark), we can infer how much
there is from how fast it’s spinning, which then lets us infer how much luminosity it must have.
We measure how fast it’s spinning by measuring the width of the 21-cm hydrogen emission line,
which will be wider (due to different parts of the galaxy being Doppler shifted differently) when
the galaxy is spinning faster. Then we can measure its brightness and get the distance from the
luminosity-brightness-distance relation (brightness = luminosity / (4π× distance2 )).
• Supernovae Ia (works up to a few hundred Megaparsecs): Supernovae Ia are a different type of
supernovae than core-collapse: they occur when a white dwarf is sucking up mass from a star
that’s nearby. White dwarfs can’t be more massive than 1.4 times the mass of the Sun, because
then they can’t support their own weight and collapse, which causes a Type Ia supernova. Since
all white dwarfs collapse at the same mass, the resulting Type Ia supernova is always the same
luminosity (and it’s really bright too, so this works well to large distances). So if you measure the
brightness of a Type Ia supernova, you can get the distance to it from the luminosity-brightnessdistance relation (brightness = luminosity / (4π× distance2 )) because they all have the same
luminosity, and astronomers know from theoretical arguments what that luminosity is.
The Big Bang Model
1. What is the Big Bang Model?
• It is the idea that the universe began in a hot, dense state that was the same everywhere. It was
so dense that there was no way for the light to escape anywhere, so there were more photons than
matter particles, which means the universe was “radiation dominated.”
• The only elements that were made at the beginning of the universe were mostly hydrogen and
some helium. Every other element had to be made in the cores of stars, so the very first stars
contained only hydrogen and helium.
• When the universe started expanding, it began to cool and became less dense. When it was about
300, 000 years old, it was no longer so dense that photons couldn’t escape from the hot gas, so
it became “transparent,” which means that photons were able to travel through space instead of
being trapped in the hot gas.
• This is also when the era of “recombination” happened, which was when protons and electrons
could combine to form atoms. Before this, there were too many photons around to allow this to
happen.
• The furthest back in the universe we can see is to the point where the universe became transparent
and the photons were released to be able to travel to us. This is a background behind everything
else in the universe, which is seen in all directions. The photons from this “wall” were initially
very energetic because they came from very hot gas, but as the universe expanded they became
redshifted so now we see them as microwaves. This is the Cosmic Microwave Background.
• The universe continues to expand, with gravity working on small scales to pull clumps of matter
together in stars, galaxies, and clusters of galaxies.
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2. What is some observational evidence for the Big Bang?
• The universe is still expanding (Hubble’s Law)
• Very old (metal-poor) stars have the correct amount of helium predicted by Big Bang Model
nucleosynthesis (fancy word for making elements)
• The Cosmic Microwave Background exists
3. How old is our universe?
• About 13.8 billion years old
Expansion, Mass, and Density of the Universe
1. How do we know the universe is expanding?
• The Hubble Law: We observe galaxies that are far away are moving away from us faster than
galaxies that are close by (distance-redshift relation).
• We know how fast they’re moving because of the Doppler shift of the light coming from them.
2. What makes up the mass-energy of the universe?
• Most of it is dark energy, 67%
• Next is dark matter, 29 %
• Then the matter we can actually see, called baryons, that makes up stars, planets, galaxies, etc.,
4%
• Neutrinos and photons make up the last tiny little bit, about 0.1%
3. What is dark energy?
• We don’t really know... but if it wasn’t there, the expansion started by the Big Bang would slow
down due to gravity.
• Therefore we can infer that it is some energy that causes the universe to continue to expand, kind
of like the opposite of gravity. It pushes things apart instead of pulling them together.
• Dark energy is also sometimes referred to as the “cosmological constant.”
4. What drives the expansion of the universe?
• Dark energy, also called the Cosmological Constant.
5. What slows down the expansion of the universe?
• Gravity caused by matter in the universe, both dark matter and conventional matter like atoms
and stars.
6. What is the critical density?
• The critical density is the density of matter and energy (both light and dark matter and dark
energy) in the universe that would perfectly balance expansion and gravitational collapse.
• If the density of the universe is greater than the critical density (ρ > ρc ), the universe would
collapse in on itself as a “Big Crunch.”
• If the density of the universe is less than the critical density (ρ < ρc ), the universe would expand
forever.
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• For our universe, the density (of matter AND dark energy) is roughly equal to the critical density,
which means the universe will continue to expand at a decreasing rate until eventually it slows
down to stop. (Side note: recent observations of very distant Type Ia supernovae suggest the
expansion is speeding up instead of slowing down, so perhaps the density of our universe is a tiny
bit smaller than the critical density).
7. What is the parameter Ω (called “omega”)?
• Ω is the ratio of the actual density (matter + dark energy) of the universe to the critical density,
which determines the curvature of the universe. Ω = ρ/ρc
• Saying that Ω < 1 means the universe is hyperbolic, or negatively curved (kind of like a saddle).
• Ω > 1 means the universe is spherical, or positively curved, like a globe.
• For our universe, it turns out Ω = 1, which means the universe is flat, or zero curvature, which
means space appears the way you would think and geometry works normally.
8. How do the different mass-energies of the universe contribute to the value of Ω?
• Since dark energy takes up roughly 70% of the universe, it has a value of ΩΛ (the Λ is for dark
energy) = 0.7, which means the ratio of dark energy density to the critical density is 0.7.
• Matter (both dark matter and baryons, which are visible matter like stars and gas) makes up
roughly the other 30%, so it has a value of Ωm = 0.3, which means the ratio of matter density to
critical density is 0.3.
• If we wanted to break down the overall matter (Ωm = 0.3) into dark matter and baryons, then for
baryons: Ωb = 0.05 (predicted by Big Bang Nucleosynthesis) and for dark matter: Ωdm = 0.25.
• Since the total matter + energy density of our universe is roughly equal to the critical density,
the total Ω = ΩΛ + Ωm = 1. This, in fact, works, because 0.3 + 0.7 = 1.0. Yay!
9. If the density of matter (dark and light) divided by the critical density is 0.3 (currently measured to
be true), what would happen if there was no dark energy to make up the other 0.7 to get Ω = 1?
• Ω would not be 1, since there’s no dark energy, it would only be Ω = 0.3 from the matter. This
means that since Ω < 1, the universe would be hyperbolic (saddle shaped), and since ρ < ρc , it
would also expand forever. Since there’s no dark energy to drive the expansion, the expansion
would slow down.
10. What happens to the photons in the universe as the universe expands, and how does this impact the
amounts of matter and radiation in the universe?
• Photons redshift to lower energies.
• Since the amount of energy in photons decreases over time but the amount of energy in matter
stays the same (matter doesn’t lose energy as it expands), the relative amount of energy in
radiation decreases while the energy in mass stays the same, and the universe shifts from being
radiation-dominated to being matter-dominated.
11. How do we measure the expansion of the universe and how it changes over the age of the universe?
• We look at the Doppler shifts of distant galaxies to determine how quickly they are moving away
from us. If this speed is higher than expected, then the universe was expanding faster in the past
(slower now). If the speed is slower than expected, the universe was expanding slower in the past
(faster now).
• This requires us to know the distance to these galaxies by some method other than Doppler shifts
so that we can determine the redshift-distance relation. Usually we can use things like Type Ia
supernovae, which is the distance measurement that works best at very large distances (see above
section on the Distance Ladder).
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Large Scale Structure
1. What is large scale structure?
• It is the clustering of galaxies and clusters of galaxies due to mutual gravitational attractions.
2. Does structure in the universe increase or decrease as the universe grows older?
• The amount of structure increases over time, because matter pulls together into denser regions
due to gravitational attraction. It takes a long time for galaxies and galaxy clusters to traverse
the large distances necessary for this to occur, so structure only increases with time.
3. Why doesn’t the expansion of the universe due to dark energy destroy large scale structure?
• Dark energy causes expansion on much larger scales than gravity works. Gravity is quite strong on
small distances, (“small” here meaning on the size of galaxy clusters), strong enough to overcome
the expansion of dark energy and contract into galaxy clusters instead.
4. The Cosmic Microwave Background is very smooth, meaning it is pretty much the same temperature
everywhere. However, we see large scale structure in our universe. Why is it hard to reconciliate these
two facts, and what is the solution?
• The CMB, which shows us how the universe was in the past, is very smooth, but our universe
today has large scale structure so it’s clumpy. This means something must’ve happened between
now and then that caused the universe to get clumpy.
• Of course, there is something that causes structure to grow: gravity!
5. What are the largest structures in the universe?
• Filaments or walls connecting the clusters. Clusters have the most mass but filaments stretch
very far.
Galaxy Classification
1. Who first came up with the galaxy classification system, and what is it based on?
• Hubble first came up with the system that we still use today
• It’s based on the appearance and shape of the galaxy
2. What are the types of galaxies in the classification system?
• Elliptical galaxies: Large collections of stars without any sort of features; no disks or spiral arms,
no visible dust lanes. Varying amounts of ellipticity from spherical to very flat and oval.
• Spiral galaxies: Central bulge of stars surrounded by a flattened disk made up of spiral arms. The
arms have more dust and stars than other regions of the disk. There is also a sparse halo of stars
in a sphere around the disk.
• Barred spiral galaxies: Like spirals, but with a bar-shaped nucleus instead of just a bulge in the
center.
• Irregular galaxies: Doesn’t fit into either elliptical or spiral classification. Usually dwarf galaxies
(smaller galaxies) are classified this way, since they’re not large enough to form a coherent disk
or ellipse.
3. How old are the stars in each type of galaxy?
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• Elliptical galaxies have very old stars and no ongoing star formation. This makes them appear
red, since big, bright, blue stars don’t live very long.
• Spiral galaxies have ongoing star formation, which makes them appear blue. Blue stars are big
and bright, and don’t live very long, so you only see them in galaxies that are still forming stars.
4. What kind of galaxy is the Milky Way?
• Barred spiral
Exoplanets and Life in the Universe
1. What is necessary for life as we know it?
• Amino acids are required for all life forms that we know of, specifically in the production of DNA.
• Water, methane, ammonia, and electricity can combine to form amino acids.
2. What was the experiment that showed a primitive atmosphere can produce amino acids?
• The Miller-Urey experiment combined some primitive chemicals like water, hydrogen, nitrogen,
and carbon dioxide and ran an electric current through them. Amino acids, the building blocks
of DNA, formed. We think this is how the necessary building blocks of life formed on our planet.
3. What is necessary for reproduction of living organisms?
• DNA, which carries the genetic code that tells every living organism how to work, must be
self-reproducing. This is a chemical process that is absolutely necessary for life to continue its
existence.
4. What is the Drake Equation, and which parameters in it can we actually observe?
• It gives the number of advanced civilizations that could exist at any given time for a galaxy.
• N = (star formation rate) × (fraction of stars with planets) × (average number of planets per star
that can support life) × (fraction of life-supporting planets that actually develop life)×(fraction of
planets with life that develop intelligent life) × (fraction of civilizations that develop technology
that releases signals into space) × (length of time a civilization sends signals into space)
• We don’t know most of these parameters. The only one we know for sure is the star formation
rate of the Milky Way, and exoplanet searches can help us get a handle on the average number of
planets per star and the average number of planets in the habitable zone for a star.
5. In general, do astronomers think it’s possible for there to be lifeform like those on Earth elsewhere in
our galaxy? Why or why not?
• Absolutely! There are lots of stars similar to our Sun, and we know from recent planet searches
that lots of stars have lots of planets.
• We can also see that new planetary systems are forming all the time, so even more planets are
out there than we can find!
• The trouble is actually finding signs of life... we can find planets that are similar to the Earth
that may have life, but we can’t get to them and we can’t tell much more about them, so we
really can’t know if there’s life unless they send us a radio signal.
6. What are the ways we determine a star might have a planet orbiting it?
• Radial velocity: We use Doppler shifts of absorption or emission lines of the star to see how the
star “wobbles” due to the gravitational pull of a planet.
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• Transits: Planets block out light from the star when they pass between the star and us.
• Microlensing: Gravitational lensing (thanks to Einstein’s general relativity) of a star as it passes
behind another star.
7. What is direct imaging of a planet?
• Once we know that a star has a planet around it using one of the other detection methods, we
can carefully block the light from the star from reaching the telescope and take a picture of just
the planets around it.
• This is really hard to do because the star is always significantly brighter than the planets, and
exactly blocking out the star without blocking out the planets is hard.
8. What is the easiest kind of planet to find with all of the detection methods?
• Very large planets will either cause the star to wobble more with their large mass, thus producing
a greater radial velocity, or will block out more light from the star during a transit with their
large size. Therefore, big planets are easier to detect.
• Planets that are very close to their stars will transit more often (sometimes once every few days!),
which increases the probability of seeing it at any time that you happen to be looking at the star.
This is also true for radial velocity detections. Therefore, planets with very short periods are
easier to detect.
9. How do planets form?
• Not all of the giant gas and dust cloud that forms a star will go into the star itself. Some of it
goes into the protoplanetary disk, which is a disk of material surrounding a star.
• If there are enough metals in the disk, planets will start to form out of it.
• Bigger and bigger rocks stick together until eventually they build up to the size of planets.
10. How is our Solar System different from other planetary systems we’ve found? Why is this a problem
for planetary formation theory?
• Most of the systems we’ve found have very massive gas planets, like Jupiter in size and composition, in very, very close to their host star. These are called “hot Jupiters.”
• Our Solar System obviously doesn’t have any of these. All our planets are pretty far away from
the Sun, and even the closest ones are pretty small and rocky, not gas giants.
• This poses a problem to the theory of planetary formation, because it is generally thought that
gas giant planets, like Jupiter, need ice to form, and ice just can’t survive that close to the star.
Maybe the planets migrated there after forming? We’re not sure.
11. Are planets possible around metal-poor stars?
• Possible? Yes. Likely? Absolutely not. Most theories of planet formation require there to be
heavy metals, like iron, in the protoplanetary disks.
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