Definition:Newtonian Potential

Theorem
Let $R$ be a region of space.

Let $S$ be a scalar field over $R$ such that:
 * $\forall \mathbf r \in R: \map S {\mathbf r} = \dfrac k r$

where:
 * $\mathbf r $ is the position vector of an arbitrary point in $R$ with respect to the origin
 * $r = \norm {\mathbf r}$ is the magnitude of $\mathbf r$
 * $k$ is some predetermined constant.

Then $S$ is known as a Newtonian potential.