Mechanism analysis of the DRO low-energy transfer problem: An energy perspective

The 2:1 resonant distant retrograde orbit (DRO), known for its long-term stability and global accessibility, holds strategic significance in current Earth–Moon space mission explorations. This paper conducts a comprehensive analysis of the problem of low-energy transferring into 2:1 DRO using the weak stability boundary (WSB) and lunar gravity assist (LGA) in the planar bi-circular restricted four-body problem (BCR4BP). The transfer process is categorized into three phases: the Earth–Moon transfer, Sun–Earth weak stability boundary transfer, and DRO low-energy capture. Addressing key questions, our study investigates: (1) Under what LGA conditions can the spacecraft reach the approximate area where the WSB region is situated? (2) How do trajectories, upon reaching the region where the WSB is located, return to the vicinity of 2:1 DRO, potentially facilitating low-energy DRO insertion? Our study involved a comprehensive analysis of the spacecraft's changes in Earth–Moon mechanical energy and Jacobi energy during the entire transfer process. This analysis yielded the energy and geometric conditions necessary for potential low-energy DRO insertion, effectively filtering out numerous impractical candidate trajectories and enhancing computational efficiency. In this paper, the geometric condition is referred to as the low-energy transfer gateway (LETG). Using the LEGT as the stitching interface, a significant number of feasible solutions were obtained effectively for bi-impulse DRO transfer trajectories through differential correction, some of which were previously undiscovered.