Analytic expressions for gravitational inner multipole moments of elementary solids and for the force between two rectangular solids

TL;DR

This paper provides explicit formulas for gravitational multipole moments of elementary solids and the force between rectangular solids, aiding precise gravitational calculations for complex objects and space instruments.

Contribution

It introduces new analytic expressions for gravitational moments of elementary shapes and the force between rectangular solids, enhancing modeling accuracy.

Findings

Analytic formulas for multipole moments up to l=5 for 11 shapes.

Explicit expression for gravitational force between two rectangular solids.

Facilitates precise gravitational analysis of complex instruments.

Abstract

We give analytic expressions for the gravitational inner spherical multipole moments, q_{lm} with l <= 5, for 11 elementary solid shapes. These moments, in conjunction with their known rotational and translational properties, can be used to calculate precisely the moments of complex objects that may be assembled from the elementary shapes. We also give an analytic expression for the gravitational force between two rectangular solids at arbitrary separations. These expressions are useful for computing the gravitational properties of complex instruments, such as those used in equivalence principle tests, and in the gravitational balancing of drag-free spacecraft.