The differential equation that describes foce fields
Poisson found that the distribution of a force such as the acceleration of gravity g in space can be expressed as the space differential of a "potential" Φ:
where R denotes the space vector with the Cartesian coordinates (i,j,k). The potential is then determined through "Poisson's equation." In the case of gravity Poisson's equation is
where G is the gravitational constant and ρ the density of the medium.