Search strategy for lunar gravity assist escape trajectories based on dynamical analysis in the three-body problem

With the growing interest in deep space exploration, the cislunar space has attracted increasing attention as the first stage to deep space. Interplanetary transfers from Earth-Moon space rely on efficient escape trajectory design. Substantial research has been dedicated to this topic, including approaches such as lunar gravity assist (LGA). In this context, this paper develops an efficient search strategy for lunar gravity assist escape trajectories within the circular restricted three-body problem, built upon a detailed investigation of underlying dynamics. The analysis begins with the identification of LGA escape trajectories, then a comprehensive analysis of the identified trajectories is conducted by deconstructing each into Earth-Moon transfer and LGA escape segments. The numerical simulation shows that the perilune phase angle is a pivotal parameter, and the effect of LGA becomes increasingly significant as the Jacobi constant decreases. The dual requirements of both segments confine the most feasible LGA perilunes to a narrow region characterized by small perilune radius and perilune phase angle near 3 π /2. Building upon the numerical results, analytical expressions were derived by assuming that the trajectory within the Moon’s sphere of influence follows a two-body orbit, which closely match numerical simulations. Finally, a search strategy for LGA escape trajectories is proposed combining analytical expressions and numerical conclusions, and its effectiveness is demonstrated. This strategy achieves a favorable trade-off between solution quality and computational efficiency, producing near-optimal results in less than 0.2% of the computation time required by purely numerical searches.