A fast calculation method for three-impulse contingency return trajectory during the near-moon phase based on differential algebra

Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions, a fast calculation method for three-impulse contingency return trajectories is proposed. Firstly, a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point. Secondly, a calculation model of three-impulse contingency return trajectories is established. Then, fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the two-body trajectory dynamics model and perturbed trajectory dynamics model. Finally, the performance of the proposed methods is verified by numerical simulation. The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition. Due to its high efficiency, the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously. These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.