Global search for periodic orbits in the irregular gravity field of a binary asteroid system

Periodic orbits are important keys to understand the motion of a massless particle in the vicinity of a binary asteroid system. Due to the complex gravity generated by the irregular-shaped asteroids, it is difficult to generate periodic orbits with an analytical method, except with the linearized dynamics in a small region around the libration points. This paper has presented a numerical method to search the three-dimensional periodic orbits in a global space. The grid searching method is used to find nearly periodic orbits, and then the shooting method is used to get the accurate periodic orbits. The method is applied to the binary asteroid (66391) 1999 KW4 to solve the periodic orbits in the vicinity. The periodic orbits are then classified into five categories according to their shapes and locations. The search method can also be used to find periodic orbits in the vicinity of other binary systems.