Review Questions for Midterm 1: Math and Units -------------- This is the square root of 10^16. -> 10^8 This is the unit that measures a different quantity than the others: millisecond, light-minute, and AU. -> millisecond --- Explanation: Millisecond is a unit of time; the others are units of distance. This is the population of the Earth (six billion) expressed in scientific notation. -> "six times ten to the nine" If x/50 = 40/1000, this is the value of x. -> 2 There are this many kilometers in 100 angstroms. -> 10^-11 This is the ratio of areas of a circle with radius of 3 and a circle with a radius of 2. -> 9/4 Light, Spectra -------------- "Electromagnetic radiation" is a fancy way of saying this common term. -> Light --- Note: Of course, EM radiation also includes radio waves and gamma rays so on, which while sometimes also called "light", the term "light" often is meant to only refer to visible light only. But fundamentally it's all the same thing; only the wavelength (and frequency and energy) differs. This quantity is inversely proportional to the frequency of a wave. -> Wavelength This is the region of the spectrum in which people emit most of their radiation. -> Infrared The Doppler effect is caused by this. -> Velocity along the line of sight [Draw an energy level diagram on the board with three levels, labeled with: E(1) = 0, E(2) = 3, E(3) = 4.] The transition between these two energy levels will generate the photon with longest wavelength. -> Level three to level two. --- Explanation: remember, for a photon, (Energy) = (Planck's constant) x (frequency), and (speed of light) = (frequency) x (wavelength). So the longest wavelength photon will have the shortest frequency and therefore the *lowest* energy, which in this example would come from the transition E(3) -> E(2) (1 unit of energy.) Because the star Arcturus is a distance of 37 light years from Earth, we see it as it appeared in this year A.D. -> 1967. A star three times hotter than the Sun will emit most of its radiation in this waveband. -> Ultraviolet This is the ratio of the speed in vaccuum of a visible photon with wavelength 5000 Angstroms and a radio wave with wavelength 50 cm. -> One ("they're the same" also presumably OK) When we finally get it working and manage to view a star with our new 14" telescope, this is how much brighter it would appear than when viewed with our old 8" telescope. -> (14/8)^2 = (7/4)^2 = 49/16 = ~3 times This is the factor by which the peak frequency of an object (the frequency at which it emits the most radiation) changes when you double its temperature and triple its surface area. -> 2 --- Explanation: From Wien's law, the peak wavelength is inversely proportional to the temperature - so when we double the temperature the peak wavelength is halved. But because frequency is inversely proportional to wavelength, this means that the frequency doubles. The Moon -------- This occurs when the Earth's shadow falls on the moon -> Lunar Eclipse The number of high tides in a day -> 2 This allows you to see the dark part of a crescent/quarter moon. -> Earth Shine (light from the Sun reflected off the Earth and then off the Moon, and finally back to the Earth again for us to see it.) If the Sun were twice as large, the Moon's distance from Earth would have to change by this factor for there to still be total solar eclipses. -> One half This is the value of the ratio of the moon's period of rotation to the period of its orbit. -> One --- Explanation: Because the Moon always shows us the same face, it must rotate at the same rate at which it revolves. This is where you would look to see a new Moon. -> Near the Sun (or, at night, below the ground... were that actually possible.) This is the oldest region of the moon. -> Lunar highlands --- Explanation: The highlands are more cratered than the maria, and therefore older (by a few hundred million years). Note that this just refers to the age the surfaces were formed, though - the maria are large lava flows that took place more recently than the solidification of the rest of the moon, so we say they're younger.) Planets ------- This rocky body shows evidence of a water-like liquid having flowed recently on its surface. -> Mars (or Earth!) This is the most volcanically active body in the Solar System -> Io This planet has the highest orbital velocity around the Sun. -> Mercury This planet has the hottest surface of any planet in the Solar System. -> Venus This is the second largest satellite in the solar system and the only one with a fully developed atmosphere -> Titan This property of Io's orbit, in addition to its small distance from Jupiter, are responsible for its extreme volcanism. -> Elliptical (and close to Jupiter) This is the largest known Kuiper belt object. -> Pluto These two planets most closely resemble the composition of the Sun and the solar nebula -> Jupiter and Saturn This feature did not coalesce into a moon due to a nearby planet's tidal forces. -> Saturn's rings --- Note: The asteroid belt was also prevented from forming a large object due to the influence of a nearby planet, but we wouldn't call the resulting object a moon. Also, the asteroid belt had more to do with Jupiter disrupting the orbits and causing energetic collisions (that shattered the forming planetoids into fragments) than tidal processes that actually prevented things from coalescing. The rings around Uranus were discovered by careful observations of this object. -> A (background) star. You can only see these planets close to the horizon (45 degrees or less). -> Mercury and Venus. --- Explanation: Because they are close to the Sun, Mercury and Venus are only high in the sky during the day when we cannot see them. Galileo, Kepler, Newton, and others ----------------------------------- Copernicus was the first person to put this at the center of the solar system. -> the Sun Kepler discovered that the shape of planets' orbits are ellipses with this at one focus and this at the other. -> the Sun and nothing According to Kepler, planets orbit in ellipses with this located at the ellipse's center. -> Nothing --- Explanation: The Sun is at one focus, but the foci are not the same as the center (except in the case of a circle.) According to Newton's 3rd law, this is the ratio of the force the Sun exerts on Jupiter to the force Jupiter exerts on the Sun. -> 1 --- Note: You can also use the formula for Newton's law of gravitation to show that the forces are the same. If Galileo had been wrong and the Sun and planets went around the Earth, we would never see Venus in this phase. -> Gibbous --- Explanation: Because Venus went around the Earth in the geocentric model (but never strayed far from the directon of the Sun), it could never go behind the Sun and would therefore only appear to us as a crescent, never gibbous or full. ("Full" is also acceptable, but even now it would be nearly impossible to observe due to Venus being right next to the Sun during the full portion of its phases.) According to Kepler's third law, this would be the period of earth if it were 4 AU from the Sun. -> 8 years From Newton's law of gravitation, your weight on Neptune, whose radius is 4 times that of Earth and whose mass is approximately 17 times that of Earth, would be this many times your weight on Earth. -> 17/(4^2) = 17/16 Asteroids, Comets, and Collisions --------------------------------- This process explains why there we see more large craters on the moon than on Earth. -> Erosion When a comet is moving away from the sun, its tail points in this direction. -> Away from the sun. Explanation: The Solar wind makes the tail point away from the Sun no matter where the comet is in its orbit. Suppose an asteroid's orbit takes it closest to the sun at a distance of 0.2 AU and farthest at a distance of 2 AU. This is its distance from the sun when it is moving the fastest. -> 0.2 AU This kind of meteoroid is thought to have form in the centers of ancient protoplanets that were blasted apart by collisions long ago. -> Iron --- Explanation: Heavy elements like iron and other metals sunk to the center of these objects while they were still molten. The outer parts are composed of lighter elements and are called stony meteoroids. The Leonid meteor shower peaks every 33 years, and was generated by a comet with a semimajor axis of this distance. -> ~10 AU --- Explanation: Meteor showers are due to a swarm of debris orbiting the Sun. If the swarm passes through Earth's orbit every 33 years, that is the period of the swarm and hence the comet that broke apart to form it. We can then use Kepler's law to calculate its semimajor axis (which is the distance from the narrow end of the ellipse of its orbit to the center of the ellipse). Earth is closest to the Sun during this month. -> January --- Explanation: While you don't technically have to know this factoid, do remember for sure that Earth is *not* closest during the Sun during our summer - the elliptical orbit of Earth has nothing to do with the seasons. Seasons are a result of Earth's axis being tilted relative to the plane in which it orbits the Sun. Bonus question: The Sun is 400 times further away from Earth than the Moon. This is its mass in Earth masses using Newton's version of Kepler's third law. -> About 400,000. --- Explanation: The idea here is not to just plug in the known masses of the Earth and Sun. Newton's version of Kepler's third law says: P^2 = [(4 pi^2) / (G (m1 + m2)] * D^3 If we assume that one object is much much more massive than the other, this simplifies to: P^2 = [(4 pi^2) / (G m1)] * D^3 We can rewrite this in terms of the mass as: m = (4 pi^2 / G) D^3 / P^2 Now, what we want is the ratio of the Sun's mass to the Earth mass. So as a ratio: m_Sun / m_Earth = [(4 pi^2 / G) D_EarthtoSun^3 / P_EartharoundSun^2] / [(4 pi^2 / G) D_MoontoEarth^3 / P_MoonaroundEarth^2] And that simplifies to: m_Sun / m_Earth = (D_EarthtoSun / D_MoontoEarth)^3 / (P_EartharoundSun / P_MoonaroundEarth)^2 The question (er... I mean, answer) states that the Sun is 400x further than the Moon, so D_EarthtoSun / D_MoontoEarth = 400. And there are about 12 months in a year (sort of), so P_EartharoundSun / P_MoonaroundEarth = 12. Therefore: m_Sun / m_Earth = (400)^3 / (12)^2 = 450,000 Which was the answer I was looking for. The actual value is 332,942, though, which is pretty close but not exact. The main reason for the difference is that the Moon actually goes around Earth a little more than 13 times in a year, not 12. [Due Earth's motion around the Sun, the Moon has to move a little "extra" in its orbit (that is, more than a full revolution) for it to return to the same phase (one month). This all adds up to one less month (phase cycle) in a year than a revolution.] There's also a small error due to neglecting m2 in the equations above. This one is obviously a fairly tough question and is much harder than anything you'll see on the midterm. However, as everything here comes out stuff we covered in class, it wouldn't be a bad idea to work through it a bit and see if you can follow the description above all the way through.