General Dynamics of Restricted Full Three-Body Problem Near Binary Asteroid System

The Restricted Full Three-Body Problem (RF3BP) characterizes the dynamics of a spacecraft in the vicinity of a binary asteroid system. Accounting for the time-varying separation between the two components, this paper develops a novel formulation of the RF3BP in a pulsating–rotating frame to explicitly capture the perturbations arising from nonuniform pulsation, nonspherical gravity, third-body solar gravity, and solar radiation pressure. The acceleration and jerk of the secondary body relative to the primary body are derived through a potential derivatives approach to fully characterize the pulsation effect. To provide additional insight into these perturbations, finite-time bounded orbits near the binary system are investigated. This study introduces an algorithm that employs a hierarchical sequence of numerical shooting procedures to transition from periodic orbits in the circular restricted three-body problem into bounded motion under higher-fidelity dynamics models. Numerical simulations for the Moshup–Squannit system demonstrate that the pulsation effect is generally significant throughout the vicinity of the binary asteroid system. Furthermore, comparisons between bounded orbits with different fidelity confirm that such pulsation can exert an influence on a spacecraft comparable to non-spherical gravity that is typically regarded as the most dominant factor.