Dynamical Model of Binary Asteroid Systems Using Binary Octahedrons

TL;DR

This paper presents a detailed dynamical model of binary asteroid systems using binary octahedrons, accounting for irregular shapes and complex motions, with high-precision calculations revealing the influence of secondary gravitational forces.

Contribution

The study introduces a novel binary polyhedron method for modeling binary asteroid dynamics, incorporating higher-order potential calculations and detailed motion analysis.

Findings

The model accurately predicts the trajectories and angular velocities of binary asteroids.

Gravitational influence of the secondary significantly affects primary's orbital and attitude motion.

High precision in energy and momentum calculations confirms the model's reliability.

Abstract

We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of total angular momentum and total energy indicate the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful for understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.