Chapter 2. Motion of the Planets
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~ ~ ~ CHAPTER 2 Motion of the Planets 33. Why are the planets called celestial "wanderers"? 34. Why are the positions of planets not shown in standard star charts? 35. During the course of a year the Sun moves across the star field through the twelve signs of the Zodiac. Name three constellations of the Zodiac. 36. Describe personal observations of one or more planets that you have made during the past six months. 37. During the historical development of an understanding of planetary motion, one of the following persons was the most influential in advocating the heliocentric hypothesis. Which one? (a) Copernicusj (b) Tycho Brahej (c) Aristotlej (d) Ptolemy. 38. What is the principal conceptual difference between the Ptolemaic and Copernican models of planetary motion? 39. What is the single most significant objection to Ptolemy's model of the solar system? 6 Motion of the Planets / 7 40. Explain briefly whether or not Ptolemy's model of planetary motion is compatible with Newton's law of gravitation and with his three laws of motion. 41. In their simplest forms the geocentric and heliocentric hypotheses of planetary motion are geometrically equivalent. In what sense is the heliocentric hypothesis superior? 42. Consider two planets of the solar system, Earth and Mars: (a) According to the heliocentric hypothesis advocated by Copernicus, the planets Earth and Mars revolve uniformly, but at different rates, in the counterclockwise sense along separate circles of different radii, each centered on the Sun. (b) According to the geocentric hypothesis of Hipparchus and Ptolemy, Mars revolves at a uniform rate in the counterclockwise sense along a small circle (the epicycle) whose center, in turn, revolves at a uniform rate in the counterclockwise sense along a larger circle (the deferent) centered on the Earth. For the sake of a simple comparison, assume that all motions occur in the same plane. Further (c) Under hypothesis (a): Let the orbit of Mars have a radius 1.59 times that of the orbit of the Earth; and let the sidereal period of revolution of the Earth be one year and that of Mars be two years. (d) Under hypothesis (b): Let the respective sidereal periods of revolution of Mars along the epicycle be one year and of the center of the epicycle along the deferent be two years and let the respective radii of the epicycle and the deferent be 1.0 and 1.59 units. Geometric equivalence of (a) and (b) is demonstrated if the radial distances between the two planets and the celestial longitude of Mars as observed from the Earth are the same functions of time under either hypothesis. A graphical solution is suggested, though a more rigorous trigonometric solution may be preferred by some students. 8 / Motion of the Planets 43. Observations of the progression of the phases of Venus (a) support the Ptolemaic hypothesis; (b) support the Copernican hypothesis; (c) do not discriminate between the Ptolemaic and Copernican hypotheses; (d) have never been satisfactorily achieved. 44. What was the principal astronomical contribution of Copernicus ? 45. Tycho Brahe's principal contribution to astronomy was (a) his detailed observations of features on the surface of the Moon; (b) his theory of the motions of the planets; (c) his observations of the apparent motion of the planets on the star field; (d) his discovery of sunspots. 46. In the early history of astronomy, some people believed that the Sun revolved about the Earth and others believed that the Earth revolved about the Sun. Which view is "correct" and why? 47. Which one of the following persons was the first to recognize the correct geometric form of the orbits of the planets? (a) Tycho Brahe; (b) Copernicus; (c) Ptolemy; (d) Kepler. 48. Kepler derived his three laws of planetary motion (a) from Newton 's laws of motion and of gravitation; (b) following a helpful suggestion by Galileo; (c) from study of Tycho Brahe's observational data; (d) within the general context of the Ptolemaic model of the solar system. 49. Kepler discovered his three laws of planetary motion on the basis of (a) Newton's universal law of gravitation; (b) Tycho Brahe's observations of the apparent motion of planets on the star field; (c) Roemer's observations of the satellites of Jupiter; (d) the observed motion of the Moon about the Earth. 50. State Kepler's three laws of planetary motion. Motion of the Planets / 9 51. In what sense did Kepler's discovery of his first law favor the Copernican model of...