Invariant manifold theory may play a significant role in the design and optimization of low thrust interplanetary trajectories. The focus of this research is to explain how low thrust trajectories interact with invariant manifolds by analyzing the trajectories of the Europa Orbiter and the Jupiter Galilean Moons Tour. It is expected that an understanding of how the Europa Orbiter trajectory travels through the Jovian system can be obtained by comparing the trajectory to the invariant manifolds of unstable resonant orbits and quasi-periodic orbits around the Lagrange points. Once the dynamics of this trajectory are understood the effects of changes in the energy will be taken into account, and the techniques will be extended to low thrust trajectories for missions such as the Jupiter Icy Moons Orbiter (JIMO).
In this talk, I will first cover some of the general tools we use for trajectory design in the three-body problem. I will then talk about current progress in our analysis of the Europa Orbiter trajectory