The Computation of Quasiterminator Orbits in Asteroid Exploration Based on the Quasi‐Newton Method

This paper investigates the computational methods of global mapping quasiterminator orbits in asteroid exploration missions. Quasiterminator orbits can serve as a unified term for terminator orbits and their related trajectories, encompassing certain resonant terminator orbits (RTOs) as well as some quasiperiodic orbits on two‐dimensional invariant tori. Considering the microgravity gravitational field environment of asteroids, solar radiation pressure (SRP) is incorporated as one of the perturbative factors in the dynamical modeling. Due to poor lighting provided by the terminator orbit, quasiperiodic orbits and RTOs as alternatives remain stable under the influence of SRP. A computationally efficient framework based on the quasi‐Newton method is proposed, which significantly improves the efficiency of orbit computation compared to Newton’s method. The periodic orbit calculated using the multiple prediction correction algorithm is ultimately converted into a system of nonlinear equation (SNE) problem. For large‐scale matrices, solving the inverse of the Jacobian matrix can lead to reduced computational efficiency. The quasi‐Newton method avoids high computational costs by approximating the inverse matrix. The results demonstrate that the quasi‐Newton method has high computational efficiency. This study lays the foundation for orbit planning and dynamical analysis in future deep space exploration missions and opens new research directions for exploring higher dimensional invariant manifolds and their applications.