Comet-type periodic motions and their out-of-plane bifurcations in the Earth-Moon CR3BP: a computational symplectic analysis

Abstract

Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries. In this paper we first provide an analytical proof of the existence of the comet-type periodic orbits by using the classical Poincar\'e continuation method. Within this analytical approach, we also determine the Conley-Zehnder index, defined as a Maslov index using a crossing form. Then, by applying a standard corrector-predictor technique, we explore numerically the two families of comet orbits within the Earth-Moon CR3BP. We compute their stability indices, identify vertical self-resonant bifurcations of higher order periods (of multiplicity from integer multiples up to six), investigate the vertically bifurcated spatial periodic solutions, and discuss their orbital characteristics. We also describe the orbits that are in resonance with the Earth and the Moon. We illustrate our main results in the form of bifurcation graphs, based on symplectic invariants, that provide a topological overview of the connections of the bifurcated branches, including bridge families.