ASTR 1110H Fall 2004 Exam 1 Solutions - September 24, 2004 Short answer questions (2 points each): 1. What is the definition of an Astronomical Unit? It is the average distance between the Earth and the Sun. 2. What is the cause of the seasons on Earth? The tilt of the Earth s rotation axis. 3. The Full Moon phase occurs every month; why isn t there a lunar eclipse every month? Because the Moon s orbit is slightly inclined relative to the orbit of the Earth around the Sun. 4. What information/observation did the ancient Greeks use to measure the ratio of the Earth-Moon distance to the Earth-Sun distance? Don t explain how they did it, just state what they used. The first- and third-quarter phases of the Moon. 5. What information/observation did the ancient Greeks use to measure the relative sizes of the Earth and the Moon? Again, don t explain how they did it, just state what they used. The size of the Moon compared to the Earth s shadow during a lunar eclipse. 6. How does the Geocentric model explain retrograde motion? With the help of epicycles and deferrents. 7. How does the Copernican model explain retrograde motion? By placing the Sun at the center, the Earth laps more distance planets. 8. What revolutionary ideas were introduced by Copernicus and by Kepler? Copernicus introduced the idea of a heliocentric universe and Kepler introduced the idea of elliptical orbits. 1
9. Consider the following three atoms: Atom-1 has 7 protons and 8 neutrons; Atom-2 has 8 protons and 7 neutrons; Atom-3 has 8 protons and 8 neutrons. Which two are isotopes of the same element? Atoms 2 and 3, because they have the same number of protons. 10. What are the two requirements for thermonuclear fusion to occur in the center of the Sun? High temperature and high density. 11. Which object radiates more energy per area: a large, cool object or a small, hot object? What is the basis for your answer? The small, hot object because the Stefan-Boltzmann law depends only on temperature and is independent of size. 12. What is the significance of the number 0.0071 in the thermonuclear fusion process? It represents the fraction of hydrogen mass that is converted into energy. 13. Is the presence of ozone in the Earth s atmosphere good or bad? Why? Good, because the ozone absorbs the Sun s harmful UV radiation. 14. Give an example of the difference between the resolution of a telescope and its magnification. A sketch might be the most useful way of answering. Better magnification makes objects appear larger, while better resolution makes objects appear sharper. 15. Give at least one reason why telescopes using mirrors can be built to a larger size than telescopes using lenses. Mirrors can be supported from behind, making them easier to support. Also, mirrors don t have to be made as perfectly as lenses. 16. What is the difference between the way planetesimals grow and the way protoplanets grow? Planetesimals grow via collisions and sticking together, protoplanets grow via the gravitational accretion process. 2
17. Can the iron meteorites come from differentiated parent bodies? Why or why not? Yes, because the irons are metals and it s the metals of high density that sink to the center of a differentiated body. 18. In a sentence or two, explain the scientific significance of meteorites. They represent the elemental composition of the primordial solar system. 19. What role did Bode s Law play in the discovery of asteroids? Because the law indicated there was a gap between Mars and Jupiter, it led to a search for the missing planet, which resulted in the accidental discovery of Ceres. 20. Other than taking photos, name two methods by which we can determine the shapes of asteroids. Radar imaging and occultations. Slightly longer answer questions (4 points each): 21. Make a sketch of the celestial sphere showing the locations of the equinoxes and the solstices. I ll show you in class again, if you wish. 22. How did the ancient Greeks measure the size of the Earth? By noticing that the Sun at noon on the summer solstice was directly overhead (i.e., at the zenith) when standing in Syene. Meanwhile, in Alexandria, the Sun was 7º away from the zenith. This difference of 7º divided by 360º corresponded to the distance between the two cities divided by the circumference of the Earth, 2πR. Thus, they could solve for R, the radius of the Earth. 23. Suppose you lived on the Earth-facing side of the Moon and your best friend lived on the Earth. When your friend was seeing a full moon, what phase would you see for Earth? Would it be daylight or dark where you live? You d see a new Earth phase. It d be daylight. 3
24. Again, suppose you lived on the Earth-facing side of the Moon and your best friend lived on the Earth. What would you see when people on Earth were experiencing an eclipse? Answer for both solar and lunar eclipses. When your friend was seeing a solar eclipse, you d be seeing a full Earth at what you considered to be nighttime. You wouldn t see an eclipse of the Earth because the Moon s shadow is not large enough to engulf the Earth. When your friend was seeing a lunar eclipse, you d be seeing an eclipse of the Sun because the Moon is entirely within the shadow cast by the Earth. 25. What were Galileo s two most important observational discoveries and what was their significance? The moons of Jupiter, indicating that not everything orbited the Earth, and the complete cycle of phases of Venus, demonstrating that Venus had to orbit the Sun (not the Earth). 26. You get X-rays of your teeth at the dentist s office. You see visible light with your eyes. Which of these two types of electromagnetic radiation has the greater wavelength? Which has the higher frequency? Which has the greater energy? Which travels faster? Visible light has greater wavelengths than X-rays, while X-rays have higher frequencies. Since they have higher frequencies, they also have greater energies. Both travel at the same speed, the speed of light. 27. The electron in a hydrogen atom jumps from the ground state to the first excited state. Has the atom absorbed or emitted energy? Is it more energy than if it had jumped from the first excited state to the second? The atom has absorbed energy. And, yes, it is more energy than if it had jumped from the first excited state to the second, because the spacing between adjacent levels, which corresponds to energy, decreases as the levels increase. 28. Describe how magnetic fields cause sunspots. The magnetic fields interact strongly with the charged particles in the convection zone of the Sun, thus diminishing their ability to undergo convection. This lessening of convection in the strong magnetic field regions reduces the amount of energy transported to the surface, thus making those regions appear relatively dark compared to the normal photosphere. Those dark regions are the sunspots. 4
29. Which group of meteorites is more common, falls or finds? Which group (falls or finds) are the Antarctic meteorites most like? Which group of meteorites is more common, primitive stones or irons? Finds are much more common. The distribution of Antarctic meteorites is more like the falls, with the large majority of them being the primitive stones. But, of course, most of them are finds. The last question is poorly worded: the true distribution of meteorites is probably more like the falls, thus primitive stones are more common in that sense, but since finds far outnumber falls and there are more irons among the finds than there are primitive stones, then answering irons would be acceptable, too. 30. Why, despite the fact that the Kirkwood gaps are clearly demonstrable, does the asteroid belt seem to have no physical gaps in it? There are no physical gaps in the asteroid belt because the asteroids have very eccentric elliptical orbits which carry them through the gaps one might expect from the Kirkwood gaps in the orbital periods. Problems (10 points each): 31. Although the asteroid Ida is not a sphere, suppose it were shaped that way and had a radius of 20 km and a density of 2.6 g/cm 3. (a) What is the volume of Ida (in cubic centimeters)? The volume is 4/3 π R 3 = 3.35 10 19 cm 3. (b) What is its mass (in grams and in kilograms)? The mass is density volume = 8.71 10 19 g = 8.71 10 16 kg. (c) The escape speed is given by V esc = (2GM/R), where G = 6.67 10-11 m 3 /(kg s 2 ). If Roger Clemens (famous baseball pitcher) were standing on Ida, could he throw a baseball off of Ida, never to return? He can throw the ball approximately 44 m/sec. Be sure to keep all of your units straight, i.e., for this part of the problem use meters, kilograms and seconds. V esc = (2GM/R) = (2 6.67 10-11 m 3 /(kg s 2 ) 8.71 10 16 kg /20,000 m) = 24 m/s, which is less than the speed that Clemens can throw. So, yes, he could throw a baseball off of Ida. 5
32. Consider a rock that contains some U-238 (which decays into Pb-206 with a half-life of 4.47 billion years). Pb-204 is non-radiogenic (not produced by radioactive decay). (a) If we had been present when this rock first solidified and we had taken samples from different parts of the rock, would the ratios of Pb-206 to Pb-204 have been the same in all of the samples? What about the ratios of U-238 to Pb-204? Yes, the Pb-206 to Pb-204 ratios would have been the same in all of the samples, since the two are isotopes of the same element. The ratios of U-238 to Pb-204 would not have to be the same. (b) How much of the original amount of U-238 is left today if the rock formed 2.235 years ago? The half-life of U-238 is 4.47 billion years, so, using N f /N i = 1/2 (age/half-life), we get N f /N i = _ (2.235/4.47) = _ (1/2) = 0.71 = 71%. 6