Mechanism and characteristics analysis of weak stability boundary transfers to the 2:1 distant retrograde orbit

Abstract

The 2:1 resonant distant retrograde orbit (DRO) has garnered considerable attention in contemporary cislunar space missions due to its strategic importance. This study conducts a thorough analysis of the mechanisms and characteristics governing global bi-impulse Earth-DRO transfer trajectories via the weak stability boundary (WSB) in the planar bicircular restricted four-body problem. Initially, a substantial number of feasible low-energy solutions are obtained through a grid search coupled with the multiple shooting differential correction algorithm, revealing previously undiscovered trajectories. Subsequently, the global picture and Pareto front solutions are presented. The departure conditions for the global solutions are discussed separately from the perspectives of the Earth-Moon rotating frame and the Sun-$B_1$ rotating frame, along with their respective characteristics. For transfers involving a translunar phase, we analyze the distribution characteristics of relevant parameters on the perilune Poincaré section, revealing intrinsic features of the translunar trajectories. In order to deepen the understanding of the WSB transfer process, this study further explores the effect of solar perturbation along the trajectories, elucidating several mechanisms of low-energy transfer. Finally, a comprehensive analysis and summary of DRO capture trajectories are provided.