Earth–Moon Quasi-Halo Orbit Family: Characteristics and Manifold Applications

Abstract

Quasi-halo orbits in the circular restricted three-body problem are quasi-periodic orbits that exist about the periodic halo orbits. A quasi-periodic orbit is an orbit diffeomorphic to a quasi-periodic torus that moves on at least a two-dimensional manifold in phase space and does not repeat itself. Given plans for the future Lunar Gateway, the quasi-halo orbits in the Earth–moon system are of interest. About each periodic halo orbit is a one-parameter family of quasi-halos, and thus across the halo orbit family is a two-parameter family of these orbits. This work surveys the two-parameter family of quasi-halo orbits in the circular restricted three-body problem to provide a global picture of the family. Additionally, the hyperbolic manifolds of these objects are explored, and applications of their uses presented. This work contributes results and analysis of the apses, geometry, and stability of the family to evaluate the use of quasi-halo orbits in the early stages of mission design.