An expansion in power series of mutual potential for gravitating bodies with finite sizes

Abstract

This investigation offers an expansion of mutual potential between two gravitating bodies of finite size in a power series of the relative coordinates of their centres of mass; the coefficients of this power series are dependent upon the generalised products of inertia of the individual bodies which are easily computable in comparison with the similar coefficients of the conventional harmonic expansion. Our coefficients require partial derivatives of different orders of the reciprocal of the distance between the two centres of mass which also can be computed easily from the recurrence relations derived in this work. Computed results pertaining to the derivatives up to seven orders are included in a table, while our Fortran program has the capability to carry out such computations to any order. The method has been derived without assuming any approximation and is valid universally without loss of any generality.