Design of Optimal Low-Thrust Lunar Pole-Sitter Missions

Abstract

Using a thruster similar to Deep Space 1’s NSTAR, pole-sitting low-thrust trajectories are discovered in the vicinity of the L 1 and L 2 libration points. The trajectories are computed with a seventh-degree Gauss-Lobatto collocation scheme that automatically positions thrusting and coasting arcs, and aligns the thruster as necessary to satisfy the problem constraints. The trajectories appear to lie on slightly deformed surfaces corresponding to the L 1 and L 2 halo orbit families. A collocation scheme is also developed that first incorporates spiraling out from low-Earth orbit, and finally spiraling down to a stable lunar orbit for continued uncontrolled surveillance of the lunar south pole. Using direct transcription via collocation, the pole-sitting coverage time is maximized to 554.18 days, and the minimum elevation angle associated with the optimal trajectory is 13.0°.