Calculating the quasi-periodic distant retrograde orbit under the ephemeris model based on the adaptive two-level differential correction

Research on the dynamics of multi-body motion in the Earth-Moon space is a crucial area in current spacecraft motion studies. Distant Retrograde Orbits (DROs) are highly valuable trajectories in the Earth-Moon space. Under the ephemeris model, DROs will become quasi-periodic. Efficiently computing quasi-periodic DROs in the ephemeris model is a pressing issue. This paper addresses the problems of high computational time cost and significant divergence over multiple orbit cycles when calculating quasi-periodic DROs under the ephemeris model and proposes an adaptive two-level differential correction algorithm based on differential evolution. The traditional two-level differential correction selects patch points at equal intervals, while the DRO states are different with different amplitudes, choosing patch points at equal intervals is simple but not suitable for most DRO. Each quasi-periodic DRO should have its own patch points position. The adaptive two-level differential correction algorithm firstly uses differential evolution to obtain the optimal solution of the position of the patch points and then two-level differential correction is played. This algorithm significantly improving both computational efficiency and orbital convergence. Simulation results show that this algorithm significantly reduces computational costs and achieves better convergence compared to traditional two-level differential correction algorithm. This study has a reference value for the design of long-term quasi-periodic DRO, and provides a new idea for the selection strategy of patch points in the two-level differential correction algorithm and the multiple shooting algorithm.