Three dimensional, periodic, halo orbits

A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio mu, from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near the libration point between the two primaries, are there no stable orbits for certain values of mu. In that case the stable range decreases with increasing mu, until it disappears at mu = 0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing mu.