Improved Multi-Impulse Insertion Design to Elliptical Lunar Frozen Orbit for South Pole Relay Satellite Deployment

The elliptical lunar frozen orbit (ELFO) has attracted significant attention in lunar south exploration missions in recent years due to its excellent coverage of the lunar polar regions. Traditional direct insertion methods often require substantial velocity increments due to the strict constraint of the argument of perilune. To address this challenge, this paper proposes an improved multi-impulse lunar orbit insertion (LOI) method for ELFO. It takes advantage of the Earth's gravitational perturbation with multiple small impulses to adjust the argument of perilune during the LOI phase and in turn reduce the velocity increments. First, considering different engineering constraints, the translunar launch windows are identified based on a hierarchical design method, and the characteristics of different Earth-Moon direct transfer orbit types are analyzed. Next, the improved LOI method is proposed and detailed. A multi-impulse LOI optimization model is established based on the hybrid orbit model. Finally, the proposed improved LOI method is applied to design the orbit for a lunar south pole relay satellite. Simulation results show that the descent-descent Earth-Moon transfer orbit type is optimal for ELFO insertion supporting Earth-lunar south pole communication. Moreover, the proposed method achieves a total velocity increment of approximately 356 m/s over a 141-hour insertion duration. Compared to the traditional method, the proposed method saves about 33% of fuel while only extending the insertion duration by 5 days. This research could provide significant technical support for orbit insertion into ELFO and offer a valuable reference for designing the orbit in future lunar south pole exploration missions.