Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem

Abstract

We develop a computational approach for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The use of low thrust propulsion allows the spacecraft to depart from the natural dynamics and enables a wider range of transfers. We generate the reachable set of the spacecraft and use this to determine transfer opportunities, analogous to the intersection of control-free invariant manifolds. The reachable set is developed on a lower dimensional Poincare section and used to design transfer trajectories. This is solved numerically as a discrete optimal control problem using a variational integrator, which preserves the geometric structure of the motion in the three-body problem. We demonstrate our approach with two numerical simulations of transfers in the Earth-Moon three-body system.