Dynamical Systems Analysis of Planetary Flybys and Approach: Planar Europa Orbiter

摘要

THIS research seeks to reexamine Galilean moon tours usingndynamical systems techniques in the context of the planarncircular restricted three-body problem with the goal of developingntechniques that will be applicable to such tours as well as to similarnlow-thrust scenarios. The fact that dynamical systems methods maynbe applied to low-thrust trajectories was suggested by the work ofnBollt and Meiss [1]. They considered a trajectory from the Earth tonthe moon using the recurrence properties of chaotic dynamics in thenEarth–moon–spacecraft three-body problem. One of the features ofndeterministic chaos is that only a very weak force is required to effectnlarge changes in the orbits, a fact first observed by Poincaré [2]. Thenweak force immediately suggests that a low-thrust engine may benused. However, an issue with their work is that it took 2.05 years tonreach the moon from a high Earth orbit (u000160; 000 km circular radiusnabove Earth). Schroer and Ott [3] reduced the transfer time to ninenmonths, which is much more practical for actual space missions.nThey identified a sequence of unstable resonant periodic orbits usingna Poincaré section of the dynamical region between the Earth and thenmoon. By targeting the invariant manifolds of these orbits, they werenable to significantly reduce the transfer time. They specifically notednthat their targeting method is very relevant to low-thrust trajectoryndesign. None of these papers, however, noted the role of the invariantnmanifolds of Lyapunov orbits in the final ballistic capture by thenmoon depicted in their figures. These two seminal works suggest thatnresonant orbits and libration orbits both play a part in low-thrustntrajectory optimization in this energy regime.