Optimal Lunar Point Return Orbit Design and Analysis via a Numerical Three-Step Approach

Herein, the characteristics of the Moon-to-Earth (M–E) trajectory satisfying the point return orbit (PRO) conditions are analyzed and optimized. A numerical three-step approach is proposed to serve as a useful tool to generate trajectory while preparing for real-world missions. To formulate the given problem, each step properly adapts different equations of motion with design parameters suitable to each step’s primary objective. Three- and N-body equations of motion are used as a basis, and PRO is constrained by the parking orbit at the Moon and Earth re-entry corridor associated with the re-entry position. Consequently, the major trans-Earth-injection (TEI) maneuver condition at the Moon is optimized together with the right ascension of the ascending node and the argument of the latitude. Moreover, the TEI maneuver magnitude with its execution date and required time of flight is optimized to form PRO. Adopting this three-step approach, the effect of the Moon’s relative motion with respect to the Earth to form the optimal TEI condition is clearly analyzed. In addition, direct insight on the TEI condition is obtained by expressing the M–E rotating frame, which is expected to save time and effort while generating initial guesses for TEI conditions.