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 μ, from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of μ. In that case the stable range decreases with increasing μ, until it disappears at μ=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 μ.