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54.2: Gravitational Potential

Last updated

Aug 8, 2024
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- 54.1: Newton’s Law of Gravity
- 54.3: The Cavendish Experiment

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Sometimes it is useful to define a gravitational potential, which is a property of space, rather than a property of the bodies present the way force and potential energy are. To find the gravitational potential, suppose we have a mass $m$ creating a gravitational field in space. We put a small "test mass" $m_{0}$ in space near mass $m$ , determine the gravitational potential energy on the test mass due to $m$ 's mass, and divide the resulting potential energy by $m_{0}$ . The result is the gravitational potential $\mathscr{E}$ . For a point mass $m$ ,

$\mathscr{E}=-\frac{G m}{r} .$

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