Analysis of Periodic and Quasi-Periodic Orbits in the Earth-Moon System

A study was conducted to analyze periodic and quasi-periodic orbits in the Earth-moon system. Two bodies of masses m1 and m2 were assumed to rotate about their center of mass in circular orbits in a plane under the influence of their mutual gravitational attraction in the model. The objective of this model was to describe the motion of a third infinitesimal mass, representing a spacecraft. The infinitesimal mass was restricted in the plane of motion of the two primaries to simplify the analysis in the study. The technique of Poincaré surface of section was used to investigate a number of these periodic and quasi-periodic orbits. The technique helped in determining the location of the periodic orbits and their stability in terms of the maximum amplitude of oscillation. It was found that the category I orbits slowly traversed toward the moon, while the category II orbits remained near the Earth and their stability increased with increasing value of the Jacobi constant.