54.2: Gravitational Potential

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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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