In this section, we will show the basic equation describing how the gravity works.
First, compare the gravity and the static electric force.
Consider the electric field formed by a point charge at a distance from the point source as
where is the electric permittivity of the vacuum.
On the other hand, the gravitational acceleration by the point mass of at the distance
from the point mass is written down as
is the gravitational constant.
Comparing these two, replacing with and at the same time
these equations (2.6) and (2.7) are identical with each other.
The Gauss theorem for electrostatic field as
and another expression using the electrostatic potential as
lead to the equations for the gravity as
where and represent the electric charge density and the mass density.
Equation (2.11) is called the Poisson equation for the gravitational potential and describes
how the potential is determined from the mass density distribution .