The evolution characterization of libratin point orbits and application research

In the context of three-body problem, the behavior of trajectory in the vicinity of the smaller primary is difficult to predict because of the complicated gravity. The most challenging problem in preliminary design is to effiectively select an appropriate initial solution. The periapsis Poincaré maps are applied to analyze the short-term and long-term behaviors of libration point orbits in planar three-body problem. The design space is significantly reduced and classified into escape and capture regions according to the periapse location. For short-term escape orbit, the homoclinic and heteroclinic trajectory design methods are present, and two-level differential correction is utilized to solve the position discontinuity problem at the patch point. For the long-term capture trajectory, several typical periodic and quasi-periodic orbits are achieved. Furthermore, the prograde trajectory is usually quasi-periodic, and proves much more stable than retrograde trajectory. With the application of periapsis Poincaré maps, the initial state corresponding to different type of trajectory is quickly determined, which provides a fast and available design tool for specific mission.