A review of periodic orbits in the circular restricted three-body problem

This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem (CRTBP), which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model. It focuses the attention on periodic orbits in the Earth-Moon system. This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies. Firstly, simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized, and periodic orbits around Lagrange points, either planar or three-dimensional, are intensively studied during past decades. Subsequently, stability index of a periodic orbit and bifurcation analysis are presented, which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals. Then, the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits, as well as constructing database of periodic orbits by numerical searching techniques are also presented. For those unstable periodic orbits, the station keeping maneuvers are reviewed. Finally, the applications of periodic orbits are presented, including those in practical missions, under consideration, and still in conceptual design stage. This review article has the function of bridging between engineers and researchers, so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem (RTBP). At the same time, it can also provide some technical thinking for general researchers.