Libration points are the five equilibrium solutions in the circular restricted three?body problem (i.e.CRTBP), and there are many periodic orbits around them. Studies on the probes moving around orbits in the vicinity of the libration points have theoretical significance and important applications for deep space explorations.From the view of modal motion, the periodic orbits are analyzed, and the polynomial series are used to derive the approximate relationships in different directions during periodic motions, which provides a new point of view to investigate the dynamics and analyze the overall characteristics of the whole system with general rules. Meanwhile, it also provides the theoretical basis for analyzing the orbits characteristics and the references of the spacecraft orbits under the actual dynamic models. The methodology of deriving topological relationships has the potential to be extended to Elliptical R3BP in three dimensional cases or orbits around the collinear libration points.