Optimal Low Thrust Trajectories for Planetary Capture

The purpose of this study is to find optimal low thrust capture trajectories in the restricted three body problem. The region of phase space which corresponds to capture by a body is bounded by the curve of zero velocity passing through the equilibrium point (Lagrange point) L2. If the spacecraft is driven to rest at L2, capture has been achieved by adding the least amount of energy. An optimal control law is developed to achieve this based on maximizing the Jacobi integral. The dynamics are then linearized around L2 for the Earth Moon system and the shooting method is used to solve the two point boundary value problem. This problem was found to be singular so the shooting method was modified to avoid making corrections along the null eigenvector. Four trajectories were found which demonstrate the optimal control law successfully caused the spacecraft to be captured by the Moon. Theses.