A linear algorithm for computing the spherical harmonic coefficients of the gravitational potential from a constant density polyhedron

摘要

A new method is proposed to derive the spherical harmonic coefficients of the contribution to the gravitational potential of a constant density polyhedron of arbitrary shape. This method relies on a set of recurrent relationships between the involved integrals, and achieves a linear complexity in function of the number of edges of the polyhedron and the number of coefficients to be computed. In this paper we present the mathematical basis of the algorithm and discuss its possible applications.