Long-term orbital evolution surrounding a binary asteroid system

Since the discovery of asteroids in the solar system, people have carried out a lot of challenging scientific research. Binary asteroid systems, which have two members orbiting around each other, are particularly prominent among the asteroids because they are believed to contain the secret of planetary evolution. They have also been the hot targets of deep space explorations, such as the DART and Hera missions. Unlike most previous studies focused on libration point orbits, this study will be focused on the perturbed Keplerian orbit surrounding a binary asteroid system in the framework of the two-body problem, which is promising for the orbit design of long-term exploration missions. In this study, a semi-analytical orbital dynamical model is established by using the averaging process. In the perturbed orbital dynamical model, both the primary's oblateness and the secondary's non-spherical gravity are considered. Several parameters are introduced to determine the applicability of the single-averaged and double-averaged models. Three constants of motion can be obtained from the double-averaged model, implying that the system is integrable and can be reduced to one degree of freedom. The equilibrium points and phase diagrams are explored to study the structure of phase space, and the Lidov-Kozai mechanism is revealed. The long-term stability is investigated from the aspect of the eccentricity oscillation, including the phase, amplitude, and its dependence on the initial orbital geometry. The stable and unstable regions in the space of orbital elements are determined with the eccentricity, orbital inclination, and initial argument of periapsis as global variables. The binary asteroid system 2003 YT1 with accurate spherical harmonic model data is used as an example for our analysis. This work expands models and results of the outer problem of the hierarchical restricted three-body problem. The models and results can also be applied to the dynamical evolution of large-scale celestial systems, such as stellar and planetary systems.