Anil final-exam review answers PDF

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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. 1

• 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. 2

• 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? 4

• 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 A = 10−10 m) to nanometers (nm, 1 nm = 10−9 m) to millimeters, centimeters, or even (˚ A, 1 ˚ 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 A(blue) to 7000 reduced range of 5000

˚ A(red) is visible, but the human eye is most sensitive in the somewhat ˚ ˚ Ato 6000 A

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 5

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 6

• 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 ...