Questions

Review Questions

1. What led astronomers to suspect that there were members of the solar system that orbit between Mars and Jupiter?

2. How did the first asteroid come to be discovered? What role did theoretical calculations play in confirming the discovery? How did this discovery differ from what astronomers had expected to find?

3. How do modern astronomers discover new asteroids?

4. What are the differences between asteroids and trans-Neptunian objects?

5. Describe the asteroid belt. Does it lie completely within the plane of the ecliptic? What are its inner and outer radii?

6. If Jupiter was not present in our solar system, would the asteroid belt exist? Why or why not?

7. What are Kirkwood gaps? What causes them?

8. Consider the early solar system when Jupiter’s semimajor axis changed as the planet migrated. Would the effect of the unstable orbital resonances (called Kirkwood gaps in the present-day asteroid belt) lead to more disruption of the original belt objects, or less?

9. Compare the explanation of the Kirkwood gaps in the asteroid belt to the way in which Saturn’s moons help produce divisions in that planet’s rings (see Section 12-11).

10. How is it possible to tell that some asteroids are nonspherical even though we do not have images of those asteroids?

11. What is the evidence that some asteroids are made of a loose conglomeration of smaller pieces?

12. What evidence links some meteorites on Earth to the asteroid Vesta?

13. The asteroid 243 Ida, which was viewed by the Galileo spacecraft, is a member of a Hirayama family. Discuss what this tells us about the history of this asteroid. Where might you look to find other members of the same family?

14. What are the Trojan asteroids, and where are they located? What holds them in this location?

15. What are near-Earth objects? What is the evidence that Earth has been struck by these objects?

16. What is the evidence that an asteroid impact could have contributed to the demise of the dinosaurs?

17. What is the difference between a meteoroid, a meteor, and a meteorite?

18. Is there anywhere on Earth where you might find large numbers of stony meteorites that are not significantly weathered? If so, where? If not, why not?

19. Scientists can tell that certain meteorites came from the interior of an asteroid rather than from its outer layers. Explain how this is done.

20. Why are some asteroids differentiated while others are not?

21. Suppose you found a rock you suspect might be a meteorite. Describe some of the things you could do to determine whether it was a meteorite or a “meteorwrong.”

22. What is the evidence that carbonaceous chondrites are essentially unaltered relics of the early solar system? What do they suggest about how the solar system may have formed?

23. With the aid of a drawing, describe the structure of a comet.

24. Why is the phrase “dirty snowball” an appropriate characterization of a comet’s nucleus?

25. What process produces jets that stream off a comet’s nucleus?

26. What did we learn from the Stardust mission about the possible connection between comets and the origins of life on Earth?

27. What did scientists learn about the structure of comet nuclei from the Deep Impact mission?

28. Why do the ion tail and dust tail of a comet point in different directions?

29. Why do comets have prominent tails for only a short time during each orbit?

30. Why is it that Jupiter and Saturn can be seen in the night sky every year, while seeing specific comets such as Halley and Hyakutake is a once-in-a-lifetime event?

31. What is the relationship between the Kuiper belt and comets?

32. What is the Oort cloud? How might it be related to planetesimals left over from the formation of the solar system?

33. Why are comets more likely to break apart at perihelion than at aphelion?

34. Why do astronomers think that meteorites come from asteroids, while meteor showers are related to comets?

35. Why are asteroids, meteorites, and comets all of special interest to astronomers who want to understand the early history and subsequent evolution of the solar system?

Advanced Questions

Questions preceded by an asterisk (*) involve topics discussed in Box 1-1 or 7-2.

36. When Olbers discovered Pallas in March 1802, the asteroid was moving from east to west relative to the stars. At what time of night was Pallas highest in the sky over Olbers’s observatory? Explain your reasoning.

37. Consider the Kirkwood gap whose orbital period is two-fifths of Jupiter’s 11.86-year period. Calculate the distance from the Sun to this gap. Does your answer agree with Figure 15-4?

38. *When the image in Figure 15-5 was made, the asteroid Ceres was 1.63 AU, or 2.44 × 10⁸ km, from the Hubble Space Telescope. (a) What was the angular size of the asteroid as a whole? (b) You can see individual pixels in the image shown in Figure 15-5. Using a ruler and the scale bar in the figure, determine how many kilometers on the surface of Ceres are contained in the width of one pixel. (c) What is the angular width of each pixel in arcseconds?

39. Suppose that a binary asteroid (two asteroids orbiting each other) is observed in which one member is 16 times brighter than the other. Suppose that both members have the same albedo and that the larger of the two is 120 km in diameter. What is the diameter of the other member?

40. The accompanying image from the Galileo spacecraft shows the asteroid 243 Ida, which has dimensions 56 × 24 × 21 km. Galileo discovered a tiny moon called Dactyl, just 1.6 × 1.2 km in size, which orbits Ida at a distance of about 100 km. (In Greek mythology, the Dactyli were beings who lived on the slopes of Mount Ida.) Describe a scenario that could explain how Ida came to have a moon.

    

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    (JPL/NASA)

41. *Assume that Ida’s tiny moon Dactyl (see Question 40) has a density of 2500 kg/m³. (a) Calculate the mass of Dactyl in kilograms. For simplicity, assume that Dactyl is a sphere 1.4 km in diameter. (b) Calculate the escape speed from the surface of Dactyl. If you were an astronaut standing on Dactyl’s surface, could you throw a baseball straight up so that it would never come down? Professional baseball pitchers can throw at speeds around 40 m/s (140 km/h, or 90 mi/h); your throwing speed is probably a bit less.

42. Imagine that you are an astronaut standing on the surface of a Trojan asteroid. How will you see the phase of Jupiter change with the passage of time? How will you see Jupiter move relative to the distant stars? Explain your answers.

43. Use the percentages of stones, irons, and stony iron meteorites that fall to Earth to estimate what fraction of their parent asteroids’ interior volume consisted of an iron core. Assume that the percentages of stones and irons that fall to Earth indicate the fractions of a parent asteroid’s interior volume occupied by rock and iron, respectively. How valid do you think this assumption is?

44. On March 8, 1997, Comet Hale-Bopp was 1.39 AU from Earth and 1.00 AU from the Sun. Use this information and that given in the caption to Figure 15-32 to estimate the length of the comet’s ion tail on that date. Give your answer in kilometers and astronomical units.

45. Sun-grazing comets come so close to the Sun that their perihelion distances are essentially zero. Find the orbital periods of Sun-grazing comets whose aphelion distances are (a) 100 AU, (b) 1000 AU, (c) 10,000 AU, and (d) 100,000 AU. Assuming that these comets can survive only a hundred perihelion passages, calculate their lifetimes. (Hint: Remember that the semimajor axis of an orbit is one-half the length of the orbit’s long axis.)

46. Comets are generally brighter a few weeks after passing perihelion than a few weeks before passing perihelion. Explain why might this be. (Hint: Water, including water-ice, does an excellent job of retaining heat.)

47. The hydrogen envelopes of comets are especially bright at an ultraviolet wavelength of 122 nm. Use Figure 5-24 to explain why.

48. A very crude model of a typical comet nucleus is a cube of ice (density 1000 kg/m³) 10 km on a side. (a) What is the mass of this nucleus? (b) Suppose 1% of the mass of the nucleus evaporates away to form the comet’s tail. Suppose further that the tail is 100 million (10⁸) km long and 1 million (10⁶) km wide. Estimate the average density of the tail (in kg/m³). For comparison, the density of the air you breathe is about 1.2 kg/m³. (c) In 1910 Earth actually passed through the tail of Comet Halley. At the time there was some concern among the general public that this could have deleterious effects on human health. Was this concern justified? Why or why not?

49. For many years it was thought that the Tunguska event was caused by a comet striking Earth. This idea was rejected because a small comet would have broken up too high in the atmosphere to cause significant damage on the ground. Explain why, using your knowledge of a comet’s structure.

Discussion Questions

50. Discuss the idea that Ceres should be regarded as the smallest dwarf planet rather than the largest asteroid. What are the advantages of this scheme? What are the disadvantages?

51. From the abundance of craters on the Moon and Mercury, we know that numerous asteroids and meteoroids struck the inner planets early in the history of our solar system. Is it reasonable to suppose that numerous comets also pelted the planets 3.5 to 4.5 billion years ago? Speculate about the effects of such a cometary bombardment, especially with regard to the evolution of the primordial atmospheres on the terrestrial planets.

52. In the 1998 movie Armageddon, an asteroid “the size of Texas” is on a collision course with Earth. The asteroid is first discovered by astronomers just 18 days prior to impact. To avert disaster, a team of astronauts blasts the asteroid into two pieces just 4 hours before impact. Discuss the plausibility of this scenario. (Hint: On average, the state of Texas extends for about 750 km from north to south and from east to west. How does this compare with the size of the largest known asteroids?)

53. Suppose astronomers discover that a near-Earth object the size of 1994 XM1 is on a collision course with Earth. Describe what humanity could do within the framework of present technology to counter such a catastrophe.

Web/eBook Questions

54. Search the World Wide Web for information about the present status of NASA’s Dawn mission. Describe one result from Vesta that is not described in this textbook.

55. Search the World Wide Web to find out why some scientists disagree with the idea that a tremendous impact led to the demise of the dinosaurs. (They do not dispute that the impact took place, only what its consequences were.) What are their arguments? From what you learn, what is your opinion?

56. Several scientific research programs are dedicated to the search for near-Earth objects (NEOs), especially those that might someday strike our planet. Search the World Wide Web for information about at least one of these programs. How does this program search for NEOs? How many NEOs has this program discovered? Will any of these pose a threat in the near future?

57. Estimating the Speed of a Comet. Access and view the video “Two Comets and an Active Sun” in Chapter 15 of the Universe Web site or eBook. (a) Why don’t the comets reappear after passing the Sun? (b) The white circle shows the size of the Sun, which has the diameter 1.39 × 10⁶ km. Using this to set the scale, step through the video and measure how the position of one of the comets changes. Use your measurements and the times displayed in the video to estimate the comet’s speed in km/h and km/s. (Assume that the comet moved in the same plane as that shown in the video.) As part of your answer, explain the technique and calculations you used. (c) How does your answer in (b) compare with the orbital speed of Mercury, the innermost and fastest-moving planet (see Table 11-1)? Why is there a difference? (d) If the comet’s motion was not in the same plane as that shown in the video, was its actual speed more or less than your estimate in (b)? Explain.