Here $g$ is the gravitational field, $G$ is the gravitational constant, and $M$ is the total mass in the volume $V$. I wonder if this formula holds for any unit system. That is, does the coefficient $4\pi$ hold true for any unit system such SI or cgs? The maxwell equations change their form with the unit system given. So I am confused.
The integral form of Newtonian gravitation as well as the differential form follows from Newton’s force law of gravity. The 4 pi factor comes from the integration over a solid angle and is therefore independent of the units used. The only time the equation would seem to change in form is if natural units are used. In that case G would become 1.