Chapter 13

# Chapter 13 - 13 Universal Gravitation CHAPTER OUTLINE 13.1...

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13 CHAPTER OUTLINE 13.1 Newton’s Law of Universal Gravitation 13.2 Measuring the Gravitational Constant 13.3 Free-Fall Acceleration and the Gravitational Force 13.4 Kepler’s Laws and the Motion of Planets 13.5 The Gravitational Field 13.6 Gravitational Potential Energy 13.7 Energy Considerations in Motion Planetary and Satellite Universal Gravitation ANSWERS TO QUESTIONS Q13.1 Because g is the same for all objects near the Earth’s surface. The larger mass needs a larger force to give it just the same acceleration. Q13.2 To a good first approximation, your bathroom scale reading is unaffected because you, the Earth, and the scale are all in free fall in the Sun’s gravitational field, in orbit around the Sun. To a precise second approximation, you weigh slightly less at noon and at midnight than you do at sunrise or sunset. The Sun’s gravitational field is a little weaker at the center of the Earth than at the surface subsolar point, and a little weaker still on the far side of the planet. When the Sun is high in your sky, its gravity pulls up on you a little more strongly than on the Earth as a whole. At midnight the Sun pulls down on you a little less strongly than it does on the Earth below you. So you can have another doughnut with lunch, and your bedsprings will still last a little longer. Q13.3 Kepler’s second law states that the angular momentum of the Earth is constant as the Earth orbits the sun. Since Lmr = ω , as the orbital radius decreases from June to December, then the orbital speed must increase accordingly. Q13.4 Because both the Earth and Moon are moving in orbit about the Sun. As described by Fm a gravitational centripetal = , the gravitational force of the Sun merely keeps the Moon (and Earth) in a nearly circular orbit of radius 150 million kilometers. Because of its velocity, the Moon is kept in its orbit about the Earth by the gravitational force of the Earth. There is no imbalance of these forces, at new moon or full moon. Q13.5 Air resistance causes a decrease in the energy of the satellite-Earth system. This reduces the diameter of the orbit, bringing the satellite closer to the surface of the Earth. A satellite in a smaller orbit, however, must travel faster. Thus, the effect of air resistance is to speed up the satellite! Q13.6 Kepler’s third law, which applies to all planets, tells us that the period of a planet is proportional to r 32 . Because Saturn and Jupiter are farther from the Sun than Earth, they have longer periods. The Sun’s gravitational field is much weaker at a distant Jovian planet. Thus, an outer planet experiences much smaller centripetal acceleration than Earth and has a correspondingly longer period. 381

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382 Universal Gravitation Q13.7 Ten terms are needed in the potential energy: U UUUUUUUUUU =+++++++++ 12 13 14 15 23 24 25 34 35 45 .
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Chapter 13 - 13 Universal Gravitation CHAPTER OUTLINE 13.1...

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