Mechanical analysis of lunar gravity assist in the Earth–Moon system

In this paper, the lunar gravity assist (LGA) is investigated under the planar circular restricted three-body problem (PCRTBP) and two-body model. In the PCRTBP, the approximate expression of energy of the LGA in a small region of the Moon is derived. The expression uncovers the mechanism and mechanical process of the LGA in the framework of the PCRTBP. Based on the expression, the change of energy during the LGA is obtained and analyzed. To solve the limitation of the expressions and complete the research range of the LGA, a numerical methodology based on the patched-conic model is presented to analyze the LGA in a large region near the Moon. This numerical methodology cannot only obtain the change of energy but also may classify the trajectories before and after the LGA. As an application, we present a method to design a special kind of double LGA orbit. The design method synthesizes the preliminary results in the patched-conic model and the optimization in the PCRTBP. We can quickly obtain abundant double LGA orbits for the Earth–Moon transfer and interplanetary spaceflight.