Self Gravity in astrobear

The governing equation is Poisson's equation for gravity:

In cartesian coordinates, the Laplacian contains only simple derivatives, i.e. does not contain any functions of position as it does in cylindrical or spherical coordinates.

Laplacian in Cartesian coordinates:

in Cylindrical coordinates:

in Spherical

and in 2.5 d:

Poisson Equation takes on a simple discretization form in Cartesian coordinates since the Laplacian contains only simple derivatives.