Abstract: On the principle of splitting the crew and cargo in a manned lunar mission, an accurate and fast approach is proposed to design the lunar module (LM) trans-lunar trajectory and to analyze the trans-lunar window’s characteristics. Firstly, based on the multi-conic method, the departure time, the argument of latitude and the acceleration impulse are chosen as the variables with the sequential quadratic programming (SQP) algorithm to calculate out the trans-lunar trajectory. Then in the Earth-centered Earth-to-Moon plane, the perilune-longitude principle is presented which could provide the appropriate initial value of the design variables. Lastly, from the characteristic analysis of the pseudo inclination, the change rule of the perilune window duration and the departure position is found. The simulation results demonstrate that the perilune-longitude principle is effective to calculate out the trans-lunar trajectory and help reveal the relationship between the low Earth orbit (LEO) and the low lunar orbit (LLO). The study’s conclusions could supply references to China’s manned lunar landing mission in the future.

Key words: Lunar module, Trans-lunar trajectory, Multi-conic method, Earth-centered Earth-to-Moon plane, Trans-lunar window