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57 Satellites and Weightlessness 45. (I) A space shuttle releases a satellite into a circular orbit 780 km above the Earth. How fast must the shuttle be moving (relative to Earth's center) when the release occurs? 47. (II) You know your mass is 62 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 77 kg. What is the acceleration of the elevator, and in which direction? 49. (II) Calculate the period of a satellite orbiting the Moon, 95 km above the Moon's surface. Ignore effects of the Earth. The radius of the Moon is 1740 km. 51. (II) What will a spring scale read for the weight of a 58.0-kg woman in an elevator that moves (a) upward with constant speed 5.0 m/s, (b) downward with constant speed 5.0 m/s, (c) with an upward acceleration 0.23 g, (d) with a downward acceleration 0.23 g, and (e) in free fall? 58 Keplel's Laws 57. (I) Neptune is an average distance of 4.5 x 109 km from the Sun. Estimate the length of the Neptunian year using the fact that the Earth is 1.50 x 108 km from the Sun on average. 59. (I) Use Kepler's laws and the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth's surface. 61. (II) Our Sun revolves about the center of our Galaxy (me 3 4 x 1041 kg) at a distance of about 3 x 104 light-years[1ly = (3.00 x 108 m/s) 0 (3.16 x 107 s/yr) - (1.00 yrl]. What is the period of the Sun's orbital motion about the center of the Galaxy? 65. (ll) Halley's comet orbits the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 545). Estimate the greatest distance of the comet from the Sun. Is it still \"in\" the solar system? What planet's orbit is nearest when it is out there? 65. (II) Halley's comet orbits the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5-45). Estimate the greatest distance of the comet from the Sun. Is it still "in" the solar system? What planet's orbit is nearest when it is out there? Halley's comet Sun FIGURE 5-45 Problem 65