The determination of the gravitational potential of arbitrary mass distribution

Numerical computation of the gravitational potential for arbitrary mass distribution in spherical coordinates is considered. It is possible to determine the potential from the spherical expansion of the Poisson integral with 1/2n²NML operations — i.e., with a number proportional to the mesh numberNML multiplied by the square of the Legendre functions of indexn. The computation of the potential based on the solution of the Poisson differential equation is discussed.