Orbital Stability Around the Primary of a Binary Asteroid System

Abstract

Orbiting the primary of a binary asteroid system is extremely challenging due to the perturbative effects of the primary’s nonspherical gravity and the secondary’s close-proximity third-body gravity. In this work, the stability of perturbed Keplerian orbits around the primary is investigated from the point of view of the long-term eccentricity oscillation. Numerical investigations indicate that the eccentricity undergoes a large-amplitude oscillation, caused by the secular perturbation of the secondary’s gravity and may cause impact. A two-degree-of-freedom dynamic model is established, based on the doubly averaged, semi-analytical orbital dynamics incorporating effects of the primary’s oblateness and the secondary’s nonspherical third-body gravity. The oscillation of eccentricity, including its phase and amplitude, and its dependence on initial orbital geometry, is investigated through the phase space structure. The results can reveal the origin of the instability, predict stable and unstable regions in the space of orbital elements, and determine the initial orbital geometry that can ensure the secular stability. The binary asteroid system 2003 YT1 is used as an example to present our verifications and analyses, and the results can also be applied to other binary asteroid systems and even planetary systems with the central body’s oblateness and the third-body gravity dominating the perturbative environments.