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The general form for the gravitational potential energy of a system consisting of two approximately spherical distributions of mass (e.g., moons, planets, or stars) is given by the equation U_g = -GMm/r. The gravitational energy is negative because the zero reference configuration is chosen as the two masses being infinitely far away from each other (r = infinity). Therefore, the gravitational potential energy for any closer configuration is less than zero.
Sections:
00:00 - Intro
01:03 - Expression for change in potential energy
02:36 - Representing force and displacement vectors
04:47 - Expression for gravitational potential energy change
07:07 - Choosing a reference for zero potential energy
10:27 - Sense check
11:31 - Why the negative sign?
12:57 - More than two masses
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