This paper derives and summarizes the analytical conditions for lunar
ballistic capture and constructs ballistic lunar transfers based on these
conditions. We adopt the Sun-Earth/Moon planar bicircular restricted four-body
problem as the dynamical model to construct lunar transfers. First, the
analytical conditions for ballistic capture are derived based on the
relationship between the Keplerian energy with respect to the Moon and the
angular momentum with respect to the Moon, 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. Then, an
optimization 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 our proposed method (100$\%$ for direct insertion
et $99.15\%$ 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 a lower impulse and shorter
time of flight compared to two conventional methods, further strengthening the
advantage of our proposed method.

Cet article explore les excursions dans le temps et leurs implications.

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