Modeling A Low-energy Ballistic Lunar Transfer Using Dynamical Systems Theory

摘要

Low-energy ballistic lunar transfers are analyzed, modeled, and constructed in this paper using dynamical systems theory. An example ballistic lunar transfer is presented here that a spacecraft may use to transfer between a 185 km circular low Earth orbit and a halo orbit about the Earth-moon L_2 point using no deterministic maneuvers apart from the translunar injection maneuver. This transfer is modeled in the patched three-body model by mapping the invariant manifolds of libration orbits. An energy analysis is presented that shows how a spacecraft's energy with respect to the Earth and moon as well as its Jacobi constant in the sun-Earth/moon and Earth-moon three-body systems change throughout the transfer. The low-energy transfer and the methods used to produce it are then validated by reconstructing the trajectory in the Jet Propulsion Laboratory's DE405 planetary and lunar ephemeris model of the solar system. Finally, it is shown that the low-energy transfer requires approximately 19.7% less A V than a conventional direct lunar transfer to the same orbit. Discussions are provided throughout the paper that consider how a ballistic lunar transfer may be a beneficial trajectory option for the transport of material between the Earth and the moon.