Constructing Four-Body Ballistic Lunar Transfers via Analytical Energy Conditions

Abstract

The current lunar exploration, particularly the regular large-scale cargo transportation in the Earth-Moon system proposes requirements for amount of low-energy lunar transfers. The conventional grid-search method to construct low-energy lunar transfers suffers from extensive computational effort and large-scale searches. To further improve the method, this paper focuses on one type of low-energy lunar transfers termed ballistic lunar transfers, and derives prior knowledge to narrow the scale of searches. The Sun-Earth/Moon planar bicircular restricted four-body problem (PBCR4BP) is adopted as the dynamical model to construct lunar transfers. First, the analytical conditions for ballistic capture are derived and summarized in form of exact ranges of the Jacobi energy at the lunar insertion point. Both sufficient and necessary condition and necessary condition are developed. These conditions suggest an important role of the Sun-Earth/Moon PBCR4BP rather than the Earth-Moon planar restricted three-body problem in achieving lunar ballistic capture. Then, a grid-search method combined with the analytical energy conditions is proposed to construct ballistic lunar transfers. Simulations shows that a high ballistic capture ratio is achieved by the proposed method (99.87% for direct insertion and 98.72% for retrograde insertion). Examining the obtained ballistic lunar transfers, the effectiveness of the analytical energy conditions is verified. Samples of our obtained lunar transfers achieves lower or comparable impulses compared to solutions obtained in the previous works. Solutions belonging to new or less-reported transfer families are also presented, and the potential engineering applications of these trajectories are briefly discussed.