Pines nonsingular gravitational potential derivation, description and implementation

Abstract

An engineering interpretation of and some minor corrections to previously completed work on a uniform representation of the gravitational potential and its derivatives (with emphasis on avoiding the usual singularity at the pole) were presented. The physical meaning of the variables was explained, the derivation of results was separated into smaller parts for easier reading, some additional recurrence relations for the derived Legendre polynomials were included and compared, and a computer program implementing this formulation was presented. Numerical experiments have shown that the use of this representation, besides removing the singularity, substantially increases the speed of the computation.