Distant stable direct orbits around the Moon

Abstract

In the present work we explore regions of distant direct stable orbits around the Moon. First, the location and size of apparently stable regions are searched for numerically, adopting the approach of temporary capture time presented in Vieira Neto & Winter (2001). The study is made in the framework of the planar, circular, restricted three-body problem, Earth-Moon- particle. Regions of the initial condition space whose trajectories are apparently stable are determined. The criterion adopted was that the trajectories do not escape from the Moon during an integration period of 104 days. Using Poincaré surface of sections the reason for the existence of the two stable regions found is studied. The stability of such regions proved to be due to two families of simple periodic orbits, h1 and h2, and the associated quasi-periodic orbits that oscillate around them. The robustness of the stability of the larger region, h2, is tested with the inclusion of the solar perturbation. The size of the region decreases, but it is still significant in size and can be useful in spacecraft missions.