The stability evolution of a family of simply periodic lunar orbits

The present work deals with a family of simply periodic orbits around the Moon in the rotating Earth–Moon-particle system. Taking the framework of the planar, circular, restricted three-body problem, we follow the evolution of this family of periodic orbits using the numerical technique of Poincaré surface of section. The maximum amplitude of oscillation about the periodic orbits are determined and can be used as a parameter to measure the degree of stability in the phase space for such orbits. Despite the fact that the whole family of periodic orbits remain stable, there is a dichotomy in the quasi-periodic ones at the Jacobi constant Cj=2.85. The quasi-periodic orbits with Cj<2.85 oscillate around the periodic orbits in a different way from those with Cj>2.85.