Long-term orbital evolution and stability surrounding a nonspherical binary system

Binary asteroid systems, consisted of two nonspherical members orbiting each other, are believed to contain the secret of planetary evolution in our solar system. The long-term exploration missions demand a thorough understanding of the orbital dynamics about the binary systems. This study is focused on the perturbed Keplerian orbits surrounding a binary asteroid system, which is modeled as an outer problem of the hierarchical restricted three-body problem. The applicability of different modeling methods and the averaging process is compared and discussed. Then, a semi-analytical orbital dynamical model incorporating two bodies' nonspherical gravity is established by using the averaging process. The equilibrium points and phase diagrams of the orbital motion are explored to uncover the structure of phase space, alongside the identification of the Lidov-Kozai mechanism. The long-term orbital stability is scrutinized in terms of eccentricity oscillation, including phase, amplitude, and the dependence on the semi-major axis. Furthermore, the existence of frozen orbits is validated through various equilibrium conditions. Finally, numerical simulations are carried out to corroborate the analytical results with the binary asteroid system 2003 YT1 as a typical example.