Extended two-body problem for rotating rigid bodies

TL;DR

This paper introduces a surface integral-based technique for efficiently solving the full two-body problem involving non-spherical rigid bodies, demonstrated on spheroids, ellipsoids, and asteroid models, with high accuracy and conservation of physical quantities.

Contribution

The paper presents a novel surface integral method for the full rigid two-body problem with non-spherical bodies, enabling fast and accurate simulations with 12 degrees of freedom.

Findings

Method accurately conserves energy and angular momentum.

Shape models have negligible effect on orbital parameters.

Angular velocity is sensitive to shape differences.

Abstract

A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but have a larger impact on the angular velocity along the $z$-direction. In all cases, energy and total angular momentum is conserved, and the simulation accuracy is kept at the machine accuracy level.