13 - Universal Gravitation

13 - Universal Gravitation - Chapter 13 Universal...

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Universal Gravitation 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 Planetary and Satellite Motion ± An understanding of the law of universal gravitation has allowed scientists to send spacecraft on impressively accurate journeys to other parts of our solar system. This photo of a volcano on Io, a moon of Jupiter, was taken by the Galileo spacecraft, which has been orbiting Jupiter since 1995. The red material has been vented from below the surface. (Univ. of Arizona/JPL/NASA) Chapter 13 389
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390 B efore 1687, a large amount of data had been collected on the motions of the Moon and the planets, but a clear understanding of the forces related to these motions was not available. In that year, Isaac Newton provided the key that unlocked the secrets of the heavens. He knew, from his first law, that a net force had to be acting on the Moon because without such a force the Moon would move in a straight-line path rather than in its almost circular orbit. Newton reasoned that this force was the gravitational attrac- tion exerted by the Earth on the Moon. He realized that the forces involved in the Earth–Moon attraction and in the Sun–planet attraction were not something special to those systems, but rather were particular cases of a general and universal attraction be- tween objects. In other words, Newton saw that the same force of attraction that causes the Moon to follow its path around the Earth also causes an apple to fall from a tree. As he put it, “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.” In this chapter we study the law of universal gravitation. We emphasize a descrip- tion of planetary motion because astronomical data provide an important test of this law’s validity. We then show that the laws of planetary motion developed by Johannes Kepler follow from the law of universal gravitation and the concept of conservation of angular momentum. We conclude by deriving a general expression for gravitational potential energy and examining the energetics of planetary and satellite motion. 13.1 Newton’s Law of Universal Gravitation You may have heard the legend that Newton was struck on the head by a falling apple while napping under a tree. This alleged accident supposedly prompted him to imag- ine that perhaps all objects in the Universe were attracted to each other in the same way the apple was attracted to the Earth. Newton analyzed astronomical data on the motion of the Moon around the Earth. From that analysis, he made the bold assertion
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13 - Universal Gravitation - Chapter 13 Universal...

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