Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric objects is given by the objects' masses and the distance between them, assuming that the mass is concentrated at the center.

Consider a point mass placed at a distance from a spherical shell. The spherically symmetric mass distribution comprises multiple concentric shells, and all the particles in a specific ring are at equal distances from the point mass.

The potential between the ring and the point mass can be obtained when the ring's mass is known. The ratio between the ring's area and the shell's area equals the ratio of their masses.

Solving the relationship between the distances, applying it, and integrating the expression gives the potential between the shell and the point mass. This expression is the same as the potential between two point masses.

If the point mass is inside the shell, then the gravitational potential is the same everywhere for all the points inside the cavity.

As the force is a derivative of the potential, the assumption also holds for gravitational force.