Abstract: The reentry trajectory optimization problem with terminal constraints and path constraints of a lunar return vehicle is considered in this paper. By defining the performance index function as a square sum of the reentry terminal position errors, the reentry trajectory design problem is transformed into the optimization problem with terminal constraints and state equation constraints. First, in the presence of the state equation constraints only, the necessary conditions of the optimization problem are obtained by using the maximum principle, and the optimal control is solved using the conjugate gradient method. Then, in the presence of path constraints, we have studied the relationship among the overload, the distance of the orbit phase, the flight path angle and the bank angle. Based on the above, a method of initial bank angle value adjustment is presented to satisfy the path constraints. This approach, with definite physical meaning and simple implementation, circumvents the shortcoming of the punishmentfunction method which involves too many adjusted parameters. Finally, a numerical example for Apollo reentry trajectory optimization is given to illustrate the effectiveness of the algorithm.

Key words: lunar return, skip reentry, trajectory optimization, property of reentry dynamics, initial value adjustment