Low thrust trajectory design for resonant flybys and captures using invariant manifolds

The application of dynamical systems techniques to the problem of low thrust trajectory design in the three-body problem has revealed a close relationship between these trajectories and the invariant manifolds of unstable periodic orbits. In this study, this relationship was explored for low thrust trajectories in the Jovian system with the focus primarily on the Jupiter-Europa three-body problem. Research in this problem was motivated by the observation that previous low thrust trajectories developed for the Jupiter Icy Moons Orbiter appeared to generally follow the invariant manifolds of periodic orbits. Two of the primary components of low thrust trajectory design in the Jovian system are the construction of resonant flybys and the capture problem. Resonant flybys were analyzed by first examining a continuous trajectory traveling between two resonances via Europa flybys. This analysis was compared to a planar Europa orbiter trajectory traveling between the same resonances while including impulsive maneuvers. In each case, the trajectories appeared to closely follow the invariant manifolds of unstable resonant orbits during the resonance transitions. It was determined that the resonant flybys were performed at energy levels where the invariant manifolds of the two relevant resonant orbits were closely related. The approach and capture problem was first characterized using collision orbit metrics, which allowed the development of general mission design boundaries. Next, it was verified that spacecraft must target a libration orbit's stable manifold in order to perform the capture. It was determined that the libration orbit's stable manifold only enclosed the desired resonant orbit for some energies, indicating that both the energy level and the resonance prior to approach must be targeted together. Finally, these same techniques were extended to analyze a low thrust trajectory. It was determined that the optimization algorithm, implemented in the Jet Propulsion Laboratory's Mystic software, produced a trajectory that closely followed the invariant manifolds of resonant orbits across energy levels. The understanding of the relationship between invariant manifolds and trajectories enabled by this analysis provides a clear indication of how low thrust trajectories may be designed and establishes a basis for the development of algorithms to use this knowledge.