Analysis of Two-Segment Lunar Free-Return Trajectories

Abstract

A precise and convenient procedure for designing the two-segment lunar free-return trajectory is presented in this paper. The trajectory characteristics are analyzed to support the lunar mission design associated with the higher inclination lunar approaches and safer returns from the moon. The concise procedure is established based on the matched conic model. An analytical algorithm is developed to compute the spacecraft state at the lunar sphere of influence to complete the conic matching. An iteration process is then adopted to generate favorable initial solutions that satisfy the constraints at injection, perilune, and Earth-entry interface. Orbital launch windows for departure from Earth, lunar encounter, and returns to Earth are established in the years 2024 and 2034. These years are chosen due to the moon’s inclination reaching a maximum in 2024 and it reaching a minimum in 2034 during a Metonic cycle. This novel trajectory enables greater lunar surface coverage than standard free-return trajectories. The trajectory can be used to lower the fuel consumption for high-latitude lunar orbiting and landing. In case a mission should be aborted in the lunar approach stage, the spacecraft can safely return without additional maneuvering. The initial trajectory is modified in a high-fidelity gravitational model and the results indicate that the difference is small and convergence is rapid.