Gravitational Potential

Gravitational potential at a point in a gravitational field is defined as the gravitational potential energy PER UNIT MASS that a small test mass would have if placed at that point:

This is exactly the same relationship that connects gravitational field strength (force per unit mass) to force itself, applied instead to energy: dividing out the test mass $m$ leaves a quantity, $V$, that depends only on the source mass $M$ and the distance $r$, and describes the gravitational field ON ITS OWN, at that point -- entirely independent of whatever particular test mass might later be placed there to "feel" it. Substituting $U(r) = -GMm/r$ from Section 7.8 and dividing by $m$,

Gravitational potential is always negative (for the conventional choice of reference point $V = 0$ at infinity), for exactly the same reason $U(r)$ is always negative: gravity is purely attractive, so bringing a unit test mass in from infinity always releases energy, leaving the system at that finite distance in a lower-energy state than at infinity. This is a genuine physical difference from, say, electric potential due to a positive charge, which is positive rather than negative -- a direct reflection of the fact that gravity has only one sign (always attractive) while electric charge has two.

Gravitational potential is a scalar quantity (unlike gravitational field strength or force, which are vectors), so when several masses are present together, the total gravitational potential at any point is simply the ordinary algebraic sum of the potentials due to each mass separately, $V_{\text{total}} = V_1 + V_2 + \cdots$ -- generally a much easier calculation than vector-adding several separate field strengths or forces. …