Energy analysis of the single impulsive Earth-Moon transfer with the temporary lunar capture

The single impulsive planar Earth-Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun-Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth-Moon transfers.& COPY; 2023 Elsevier B.V. All rights reserved.