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

Abstract

O NE of the earliest investigations of the Poincare surfaces of section method [1] to discover periodic orbits in the restricted three-body problemwas byHenon [2–5] in a number of publications. Jefferys [6] also used this method to evolve a large number of periodic orbits in the restricted three-body problem. After that, this technique has been used by many researchers to find periodic orbits in the restricted three-body problem. Some of the important contributions are by Smith [7], Smith and Szebehely [8], Tuckness [9,10], Scott and Spencer [11], Howell and Kakoi [12], Demeyer and Gurfil [13], Guilera [14], and Kolemen et al. [15]. The motivation for the present study comes from the work of Winter [16], which deals with a family of simply symmetric retrograde periodic orbits around the moon in the rotating Earth–moon–particle system in the framework of the planar circular restricted three-body problem for the Earth–moon mass ratio (0.01215). This family of periodic orbits is one particular case of the family of periodic orbits classified by Broucke [17].