Abstract
The Halo orbits originating in the vicinities of both,L 1 andL 2 grow larger, but shorter in period, as they shift towards the Moon. There is in each case a narrow band of stable orbits roughly half-way to the Moon. Nearer to the Moon, the orbits are fairly well-approximated by an ‘almost rectilinear’ analysis. TheL 2 family shrinks in size as it approaches the Moon, becoming stable again shortly before penetrating the lunar surface. TheL 1-family becomes longer and thinner as it approaches the Moon, with a second narrow band of stable orbits with perilune, however, below the lunar surface.
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References
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Breakwell, J.V., Brown, J.V. The ‘Halo’ family of 3-dimensional periodic orbits in the Earth-Moon restricted 3-body problem. Celestial Mechanics 20, 389–404 (1979). https://doi.org/10.1007/BF01230405
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DOI: https://doi.org/10.1007/BF01230405