The gravitational potential energy of a point mass m in the gravitational field of a point mass M is given by

(1)

which should be emphasized is a negative number. It should also be emphasized that this equation is not only true for a point mass M, but also for an external point of a body having a spherically symmetric mass density with total mass M, where r is the radius from the center of mass. This nontrivial fact can be proved using calculus, and was one of the highlights of Newton's Principia Mathematica.

Gravitational Multipole Expansion, Gravitational Potential, Jeans Length, Poisson's Equation, Sphere Gravitational Potential Energy