Forced Periodic Trajectory Reachable Set Analyses in the Earth-Moon System

In cislunar space, spacecraft are able to exploit naturally periodic orbits, which provide operational reliability. However, these periodic orbits only exist in a limited volume. We show that spacecraft equipped with low-thrust propulsion can follow a greater number of periodic trajectories in cislunar space. We describe and discuss methodologies for producing energy-optimal and mass-optimal, forced, periodic trajectories and the reachable sets of these trajectories for a given thrust level in the circular restricted three body problem. The energy-limited set uses a linearization about a reference trajectory and is composed of energy-optimal trajectories. The thrust-limited set uses the full nonlinear dynamics and is composed of mass-optimal trajectories. In this study, we find that the use of the linearized energy-limited, energy-optimal set of forced periodic trajectories is an underestimate of the true reachable set. We instead recommend the use of a PSO algorithm and direct collocation scheme to find the set, which provides a much tighter minimum bound.