Analytical Energy Conditions Improve Ballistic Lunar Transfer Design

This paper presents a method for constructing four-body ballistic lunar transfers using analytical energy conditions. The research addresses the growing need for efficient low-energy lunar transfers, particularly for large-scale cargo transportation in the Earth-Moon system. The conventional grid-search method for designing such transfers is computationally intensive and requires extensive searches. To improve efficiency, the authors focus on ballistic lunar transfers and derive prior knowledge to narrow the search space. They adopt the Sun-Earth/Moon planar bicircular restricted four-body problem (PBCR4BP) as the dynamical model and derive analytical conditions for ballistic capture, expressed as exact ranges of the Jacobi energy at the lunar insertion point. A grid-search method, combined with these analytical energy conditions, achieves high ballistic capture ratios. Simulations demonstrate a 99.87% capture rate for direct insertion. The resulting lunar transfers exhibit lower or comparable impulses compared to solutions obtained in previous studies. The authors also present solutions belonging to new or less-reported transfer families, highlighting their potential engineering applications. This research contributes to the development of more efficient and cost-effective lunar transportation systems, which are essential for future lunar exploration and resource utilization. The analytical energy conditions provide valuable insights into the dynamics of ballistic lunar transfers and can be used to optimize trajectory design.

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