Low thrust Earth-Moon transfer trajectories via lunar capture set

A cislunar cargo spacecraft with low-thrust propulsion traveling between the Earth and the Moon is essential for sustainable, long-term manned lunar exploration. In low-thrust Earth-Moon transfer (LTEMT), lunar capture is the primary prerequisite for spacecraft subject to the circular restricted three-body model. Therefore, this study identifies sufficient conditions for lunar capture, which are determined by the Jacobi integral and Hill's region. This paper proposes a guidance scheme that includes thrust direction, thrust efficiency, and a five-stage flight control sequence based on the variation of the Jacobi integral. The LTEMT problem is then converted to an initial value problem of a differential equation with three parameters. Lunar capture set theories (LCSTs), which are convenient for identifying lunar capture sets, are presented and proved according to the continuous properties of the ordinary differential equation. Finally, the solutions of the LTEMT trajectories departing from a geosynchronous orbit with an altitude of approximately 35,827 km are discussed for different thrust accelerations and cut-off values of the thrust efficiency. The robustness is analyzed assuming that navigation and switching time errors are present to demonstrate the adaptability of this method. The results reveal that the proposed guidance scheme and LCSTs can provide technical support for future cislunar cargo missions.