MT2 review soln - AyC10 Fall 2007: Midterm 2 Review Sheet...

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Unformatted text preview: AyC10 Fall 2007: Midterm 2 Review Sheet Nicholas McConnell This compilation of questions does not comprehensively cover the course material since Midterm 1, nor does it necessarily cover all the main ideas. But most of the questions here touch on key ideas that we hope you have learned. These may be a useful starting point to see how comfortable you are with many of the primary concepts introduced in this part of the course. Hopefully they will provoke you to ask more in-depth questions, and investigate the details as you study for the exam. CS 119-139 Why is Pluto no longer a planet, according to the International Astronomical Union’s definition? Pluto meets two of the three criteria in the IAU's 2006 definition of a planet: it does orbit the Sun, and it is spherical. However, it does not meet the criterion that it must clear other objects (except for moons and rings) out of its orbital region. Instead, Pluto orbits the Sun among many other small bodies. Collectively, Pluto and these objects make up the Kuiper Belt. Where do comets originate? The Solar System has two reservoirs of icy objects that might become visible as comets: the Kuiper Belt and the Oort Cloud. The Kuiper Belt is a ring of material beyond Neptune's orbit, centered in the same plane in which the planets orbit the Sun. Kuiper Belt objects whose elliptical orbits come particularly close to the Sun appear as comets when they partially evaporate. These are periodic comets, who approach the sun and become visible at regular intervals. The Oort cloud is a spherical collection of objects that orbit the Sun far beyond the orbits of the planets and the Kuiper Belt. Occasionally, an Oort cloud object will be perturbed in its orbit and come zooming toward the Sun. If it comes close enough, it will appear visible as a comet for the same reason (evaporation) as Kuiper Belt comets. However, Oort Cloud comets often escape the Solar System after flying by the Sun, or their orbital periods are so long that we only record one pass-by. What is the difference between a comet, an asteroid, and a meteoroid? Comets are made mostly of dust and ice; they can evaporate. Asteroids and most meteoroids are made of metal and rock. Asteroids orbit the Sun in the asteroid belt between Mars and Jupiter. Meteoroids orbit the Sun, but not in the asteroid belt. Describe what would happen if a 10-km object collided with Earth. How often does this happen? The impact of a 10-km object would be catastrophic. Utter devastation would occur for hundreds of km around the impact site. If the object landed in the ocean, it would hit the ocean floor almost immediately and cause the same devastation, additionally creating enormous tidal waves. The impact would vaporize nearby rocks and send tremendous amounts of debris in the air. Eventually, dust would circulate throughout the atmosphere, blocking sunlight and causing drastic harm to global plant life. Global temperatures would change, and all but the hardiest species would face extinction. CS 140-146 Describe the Doppler (radial velocity) method of finding extra-solar planets. What properties of the planet does it allow us to determine? What are its limitations? When a planet orbits a star, its gravity pulls on the star, causing the star to wobble in a tiny circle about the system’s center of mass. If we take a spectrum of the star’s light, we will observe a periodic trend in the Doppler shift of spectral lines: a repetitive pattern over time of redshifts and blueshifts. Once we have recorded the whole pattern, we can determine the planet’s orbital period, and use Kepler’s Third Law (assuming we know the mass of the star) to get the planet’s orbital distance. Based on the strength of the wobble, we can also determine a minimum value for the planet’s mass, but not the exact value, because we don’t know the extent to which the orbit and wobble are along our line of sight. The Doppler method is limited by time and by technology. Our best technology is currently good enough to detect planets 4-5 times as massive as Earth, but no smaller. We can only be sure a planet exists after we observe the star for an entire orbital period, so planets whose orbits take longer than 15-20 years won’t have been discovered yet. Describe the transit method of finding extra-solar planets. What properties of the planet does it allow us to determine? What are its limitations? Sometimes we get lucky and are able to observe a star when its planet is crossing directly in front of it, from our perspective. We don’t see the planet, but we are able to deduce its presence because we see the star get dimmer, and then return to its normal brightness when the planet is no longer blocking any part of the star’s disc. With this method, we can determine the planet’s physical radius. If the planet has an atmosphere, we can also learn about the atmosphere’s chemical composition, by comparing the star’s normal spectrum to its spectrum when the planet is in front of it. The transit method requires us to be looking at the right place for a short interval of time. It doesn’t give us any direct information about the planet’s mass. CS 147-153 What part of the Sun do we see in the daytime sky? How does its temperature relate to the temperature at the Sun’s center? The part of the Sun we see (except during total solar eclipses) is the photosphere. Its temperature (about 6000 K) is cooler than the center of the sun (about 15 million K). How does the Sun’s magnetic field influence sunspots? Sunspots occur in regions where the Sun’s magnetic field arches over the photosphere. The shape of the arch creates a downward pressure (magnetic pressure!) on the photosphere, and inhibits hot gas from rising to the surface of that part of the Sun. Therefore, that patch of the photosphere is cooler and appears as a sunspot. The Sun’s magnetic field changes direction every 11 years (giving a complete magnetic cycle of 22 years: 11 years per configuration), and this cycle is traced by the number of sunspots we observe. When the field is changing direction, we observe a lot of sunspots (solar maximum). In between, we observe relatively few (solar minimum). What other features of the Sun and its activity vary cyclically? Other energetic events such as flares, prominences, and coronal mass ejections vary in a cycle that corresponds to the Sun’s magnetic cycle. Every 11 years at solar maximum, we observe many of these events in addition to many sunspots. We see less activity at solar minimum. Finally, the corona’s overall shape changes in an 11-year cycle, mirroring the global shape of the Sun’s magnetic field. CS 154-159 Describe how parallax works. What does this effect depend on? Can we use it to determine the distance to all stars? Parallax is an effect we observe when we take precise measurements of the positions of stars. We use it to determine the distance to stars. Because the Earth’s location changes as it orbits the Sun, its line of sight to other objects changes. The size of this effect depends on the size of the change in Earth’s position (2 AU per six months, repeating every year) and the distance to the objects (the effect is bigger for closer objects). For the most of the stars in our galaxy, the line of sight barely changes at all: in fact, too little for our best technology to detect. But for close stars, we can detect an apparent shift in position with respect to the seemingly motionless “background stars.” If we measure the angular size of this shift (the quantity “parallax” refers to this measured angle), we can use it to determine the distance to the nearby star. As stated above, some stars are too far for us to detect their apparent motion from our changing line of sight. Therefore, we cannot use parallax to determine the precise distances to those stars. What is the difference between brightness and luminosity? How do we calculate a star’s intrinsic energy output? Luminosity is the amount of energy a light source releases per second. It is an intrinsic property of the source. Brightness is the amount of energy per second per unit surface area detected by an observer. It is proportional to the source’s luminosity but also depends on the observer’s distance from the source. We calculate the luminosity (same as “intrinsic energy output”) of stars by measuring their brightness (counting how many photons hit our camera chip) and their distance (via parallax or other methods we haven’t discussed in detail). Once we know those two quantities, we use the equation b = L / 4d2 to compute the luminosity. CS 160-168 What does it mean for a star to be on the Main Sequence? A star is on the Main Sequence when its core is fusing hydrogen into helium. During this phase, stars are mostly stable and obey well-defined relationships between their mass, luminosity, and surface temperature (note: L M4 only applies to Main Sequence stars). As a result of these relationships, Main Sequence stars lie in a diagonal strip along the temperature-luminosity (H-R) diagram, with more massive stars at higher temperatures and luminosities. Consider two stars of spectral type K. One is a red giant, and one is a main sequence red dwarf. How are these stars similar? How are they different? Is the red giant necessarily much more massive than the red dwarf? Because these stars are of the same spectral type, they have approximately the same surface temperature. However, the red giant is much more luminous and has a much larger radius. Still, a red giant is not necessarily more massive than a red dwarf. As they evolve off the Main Sequence, stars do not gain mass. Therefore, a star that has one solar mass on the main sequence will evolve into a 1-solar-mass red giant. Do stars form by themselves, or in groups? Most stars form in groups. Star formation starts in a large cloud of gas that fragments, and the individual fragments form lots of stars close to each other. These stars might have enough mutual gravitational attraction to stay together for a long time as a star cluster, but eventually they will drift apart. Additionally, some stars form in binary pairs (and binary pairs are still in clusters with other stars when they form). Binary stars usually orbit each other for their entire lives. How can we tell the difference between an old star cluster and a young cluster? Which one will have more high-mass stars? Very luminous Main Sequence stars (O-Type, B-Type, etc.) burn up all their fuel and die out very quickly compared to less-massive, less-luminous stars. If we look at a young star cluster, it may have Main Sequence stars of all spectral types, but soon the O stars will disappear, then the B stars, then the A stars, etc. By the time the cluster is very old, it will only have M and L stars left on the Main Sequence. Therefore, we determine a cluster’s age by making a temperature-luminosity (H-R) plot of all its stars. This will allow us to see what stars are in the Main Sequence (as opposed to red giants, white dwarfs, etc). Based on which spectral types are still left on the cluster’s Main Sequence, we can estimate its age. Because the stars are all at about the same distance from us and they all formed at about the same time, they are a good representative population for the age of the cluster as a whole. High-mass stars have short lives and explode in supernovae before many other stars have even finished burning up their hydrogen. Therefore, only young clusters should contain high-mass stars. Old clusters won’t have any left. CS 169-196 Refer to the Supernovae worksheet for more material on this range of course slides. What is the final stage of an evolved low-mass (less than 8 solar masses) star? What are its properties? How does it keep stable from collapse? Low-mass stars end up as white dwarfs. A white dwarf is a very compact mass made primarily of carbon and oxygen; it is the leftover core of the original star, after hydrogen fused to helium (Main Sequence phase) and helium fused to carbon/oxygen (red giant and planetary nebula phases). White dwarfs are very small compared to regular stars, and more-massive white dwarfs are actually smaller in size than less-massive ones. They are very hot initially, but very slowly cool down. White dwarfs don’t collapse because of electron degeneracy pressure. Quantum physics demands that within a certain region (in this case, the interior of the white dwarf) only so many electrons can have a certain speed (“degeneracy” refers to multiple objects having the same properties, and quantum physics sets a hard limit on how much degeneracy is allowed). If there are more electrons, they must have higher and higher speeds. In a compact object like a white dwarf, the low-speed “energy levels” fill up, and electrons are forced to move around very quickly, exerting a tremendous pressure that opposes gravity. The neutrons in a white dwarf aren’t densely packed enough to be subject to quantum physics regulations. What is left behind after a Type II supernova? How was this kind of object discovered? A few Type-II supernovae may leave behind black holes, but most leave behind neutron stars. A neutron star is an extremely small, extremely dense sphere of pure nuclear material—like a gigantic atomic nucleus. Atoms in normal matter are mostly empty space, between the nucleus and the electrons. Not so in a neutron star. Neutron stars avoid collapse by the same principle as white dwarfs, but using neutron speeds instead of electron speeds. Neutron degeneracy pressure is even more powerful than electron degeneracy pressure. Some neutron stars have strong magnetic fields and rotate. The magnetic fields “beam” energy outward along two narrow poles, and the rotation causes each pole to sweep around in a circle. From Earth, our line of sight might intersect the temporary direction of a beam, in which case we see a source that sends pulses of light out at regular intervals. The period of the pulsations was too fast to suggest anything but a rotating neutron star. Therefore, we discovered the first neutron stars as pulsars. How does the first generation of stars ever formed differ from later generations? What does this have to do with us and our planet? When the first generation of stars formed, the universe only contained the elements hydrogen and helium. Therefore, those stars were initially made of pure hydrogen and helium, but through fusion and supernovae they created heavier elements. Subsequent generations of stars thus contained a small amount of heavy elements when they formed. Because every generation of stars fuses some hydrogen and helium into heavier elements, younger stars have a higher concentration of heavier elements (but the difference is only noticeable over many generations). Earth is mostly made up of heavy elements: iron, nickel, silicon, carbon, oxygen, nitrogen, etc. Our bodies are made of heavy elements (yes, water contains hydrogen, but it also contains oxygen). These heavy elements exist because they were formed by previous generations of stars. CS 197-211 How does light interact with massive objects? According to Einstein’s theory of General Relativity, massive objects cause light to bend. A ray of light passing near a massive object will bend slightly (or, if the object is very dense, like a black hole, not so slightly) toward the object’s center. Light also loses energy and becomes redshifted as it moves away from a massive object. If I stand on the surface of a neutron star (or anything massive, but neutron stars are particularly dense and therefore cause a particularly dramatic warping of space-time) and shine a light out into space, you will observe it at a longer wavelength than I emitted it. Suppose you go near, but not across the event horizon of a black hole. What happens to you, relative to someone watching you from far away? According to General Relativity, space-time gets warped by massive objects. We don’t call it “space-time” just to sound cool (or uncool)—it’s actually a warping of space and time. Because time gets warped, as you come near the event horizon, a distant observer will see everything you do slow down. You will travel slower, move slower, emit photons less frequently, and age slower (and truthfully, if you came back to where the observer was, he would have aged more than you!). Because space gets warped, the light your body emits will be redshifted as it travels to the observer (this is the same effect mentioned above—it can be described in terms of losing energy to the gravitational field, or increasing wavelength as space gets warped). A third effect, which can be described without resorting to General Relativity, is that you will be stretched out by tidal forces— the gravity pulling on your feet (if your feet are closest to the black hole) would be stronger than the gravity pulling on your head. What if you cross the event horizon? In the scenario above, everything except for tidal stretching appears normal from your point of view; it’s the different observer who notices unusual time-slowing and redshifting effects. Likewise, if you cross the event horizon (assuming you survive the tidal stretching—which can be mild for very massive black holes—yes, more massive means weaker tidal effects in this case), you will feel like you are traveling, etc. at a normal speed. On the other hand, in the distant observer’s point of view, you will slow down so much that by the time you are at the event horizon, you will be moving infinitely slowly, and the observer will never see you cross it. Your light will also be infinitely redshifted, well beyond visible wavelengths, and you will emit photons infinitely slowly. Your fate on the other side of the event horizon may be fascinating: you might be destroyed, or spat out a wormhole into another universe, or transported somewhere else in our universe. No one knows. And because no one outside the black hole can ever see you cross, no one ever will. But, if the history of science has taught us anything, it’s “never say never.” What effects do black holes have on other astronomical objects, in real life? To be subject to the effect described above, you would have to come very close to the event horizon of a black hole. At large (a.k.a. “normal,” in the astronomical sense) distances, black holes act just like stars or any other objects of the same mass. For example, a classical question is, “If the Sun were replaced by a 1-solar-mass black hole, what would happen to Earth?” The answer: we’d stop receiving sunlight, of course, but otherwise, nothing would be different. Earth would orbit regularly at 1 A.U., just like before. When a black hole is in a binary pair with another star, it can consume gas that expands off the star’s surface. But we know that this also happens with white dwarfs and neutron stars that are close to expanding red giants. So again, black holes don’t influence other astronomical objects differently from normal stars, in the majority of cases. ...
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