Parameterized Design for Moon-to-Earth Transfer Trajectories Considering Re-Entry and Landing Constraints

A parameterized trajectory design is proposed to solve the Moon-to-Earth transfer at any given epoch, providing a fast and high-fidelity solution that considers re-entry and landing constraints without computational optimization methods. First, the re-entry and landing constraints of the re-entry trajectory are inspected by solving the quasi-Lambert problem, which reduces the solution space and allows for a fast search of all constraints without the need for optimization. The existence of a trajectory is revealed, and three reduced trajectory design parameters are introduced to connect the Earth re-entry and Moon escape trajectories. These uncoupled trajectory design parameters convert trajectory optimization into a parameter selection problem that is insensitive to the initial value selection. Subsequently, an adjustment strategy for these parameters is proposed to minimize the velocity increment of the entire trajectory, which also ensures rapid convergence with only a few updates. The numerical results of typical 3-day transfer trajectories verify that this parameterized design is suitable for the abort trajectory design for a crewed Moon mission due to its ability to design the trajectory at any given epoch and its convenience in generating a series of transfer trajectories at different times under the similar dynamics condition.