Concept of Potential

From the gravitational potential energy formula $U=-\dfrac{GMm}{r}$, the factor $-\dfrac{GM}{r}$ depends only on the source mass M (the Earth, in this case) and the location r -- it does NOT depend on the particular test mass m being considered. Because this factor is the same for ANY mass m placed at that location, it is given its own name: the gravitational potential $V_r$ of the Earth at distance r, $V_r=-\dfrac{GM}{r}.$ In these terms, the potential energy of the Earth-mass system can be re-expressed simply as (gravitational potential) $\times$ (mass placed there): $U=V_r\,m$, or equivalently, gravitational potential is defined as gravitational potential energy PER UNIT MASS, $V_r=U/m$. This idea of 'potential' -- an energy-per-unit-source-quantity field surrounding a source -- generalises to any conservative force field (for instance, electric potential plays the analogous role for the electrostatic force).

The gravitational potential DIFFERENCE between any two points 1 and 2 in a gravitational field is $V_2-V_1=\dfrac{U_2-U_1}{m}=\dfrac{dW}{m},$ i.e. the work done (or change in potential energy) per unit mass in moving between the two points. …