Families of orbits in the vicinity of the collinear libration points

Abstract

In recent years, three-dimensional periodic and quasi-periodic orbits near the collinear libration points in the Sun-Earth/Moon three-body problem have been the focus of great interest for space mission design. Thus, more effort in the astrodynamics community has been directed toward analysis and computation of families of such orbits. But families of periodic orbits in the three-body problem have been the subject of much study for many decades. The first such orbit to be employed for a spacecraft trajectory (ISEE-3) was a member of a particular type of simply symmetric three-dimensional family, i.e., a halo orbit. Thus, attention shifted to further analysis of these periodic halo families. Some of the significant work in the development of periodic solutions in the three-body problem has been reviewed and a number of the highlights from the analysis and eventual numerical computation of halo families is presented here. The halo families of periodic orbits extend from each of the libration points to the nearest primary; they appear to exist for all values of the mass ratio. Thus, this further understanding may serve to support future spacecraft mission planning as well.