This work was completed as my final project for the course: AERE 6510 Space Trajectory Optimization under Prof. Ossama Abdelkhalik. I extended the classic three-stage method for computing optimal low-thrust trajectories from low Earth orbit (LEO) to low lunar orbit (LLO) originally proposed by Pierson and Kluever (1994).

The original three-stage method systematically decomposes the complex optimal trajectory problem into simpler subproblems: maximum-energy Earth-escape and moon-capture spirals, an all-coasting translunar trajectory, and a complete optimization using a hybrid direct/indirect numerical method. Unlike the original formulation, which assumes constant thrust magnitude, my work allowed thrust magnitude to be a free variable within the optimal control framework.

Starting from the necessary conditions for optimality, I derived the modified equations and solved them numerically to obtain optimal trajectories. The classical restricted three-body problem (CR3BP) governs spacecraft trajectories and involves highly sensitive numerical computations. Our extended methodology enables a more flexible approach to modeling low-thrust cislunar transfers. Simulation results demonstrated the approach's effectiveness, yielding energy-efficient transfer trajectories that improve upon the constant-thrust assumption.