Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach

TL;DR

This paper presents a power series expansion method to accurately compute gravitational forces and torques between arbitrarily shaped bodies with complex mass distributions, ensuring fast and convergent numerical calculations.

Contribution

It introduces a rigorous power series formalism for mutual gravitational interactions of arbitrary bodies, linking inertia products to spherical harmonics coefficients.

Findings

Power series converge absolutely and reliably.

Method is suitable for rapid numerical computations.

Provides detailed relationship between inertia products and spherical harmonics.

Abstract

We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their centres of mass. The absolute convergence of all the power series developed is rigorously demonstrated. The absence of transcendental functions makes this formalism suitable for fast numerical applications. The products of inertia used here are directly related to the spherical harmonics coefficients, and we provide a detailed analysis of this relationship.