Families of Cycler Trajectories in the Earth-Moon System

Abstract

Motivated by the need for infrastructure in cis-Lunar space to support telecommunications, navigation, spacecraft servicing and astronaut rescue, periodic orbits in the EarthMoon system are computed, classified and assessed using relevant criteria. Using the planar circular, restricted three-body model, cyclers – periodic orbits that pass near the Earth as well as near or behind the Moon – are computed using three strategies. In the first, a cycler is approximated by an elliptic Earth orbit, neglecting the lunar gravity, and then differentially corrected to account for the lunar gravity. In the second strategy, a p-q resonant cycler is analytically approximated for small lunar mass as a seed for generating a family of cyclers via differential correction and continuation. In the third strategy, cyclers are constructed using homoclinic connections between unstable Lyapunov orbits associated with a libration point. The utility of these cyclers is then assessed relative to the criteria for cis-Lunar infrastructure. infrastructure beyond geostationary orbit will be needed to support Moon exploration and utilization and other future activities in the the Earth-Moon system. Anticipated elements of this infrastructure are spacecraft in low maintenance orbits that regularly visit the vicinity of the Earth and the vicinity of the Moon. Such spacecraft would serve telecommunication, navigation or astronaut rescue purposes, for examples. This need motivates the identification of appropriate periodic orbits in the Earth-Moon system to serve as the backbone of such missions. The terms cycler and cycler trajectory will be used to refer to a periodic orbit that passes near the Earth and near or behind the Moon. Previous research 1–5 has identified interesting cycler trajectories in the Earth-Moon system. Classes of periodic and resonant orbits have been determined via global search methods, 1,6,7 patched conic approaches 1,8,9 and dynamical systems theory. 10–20 The researches most directly related to our work is described further: The classification of planar, simple periodic symmetric families of orbits in mission designs in the Earth-Moon system was studied by Lo and Parker. 16 This study considered the planar periodic orbits pierce orthogonally the x-axis in the rotating frame exactly twice per orbit. Continuation was used to explore several families of this class of planar orbits in the restricted three-body problem, producing the invariant manifolds of the unstable orbits in each of these families. While some of these orbits considered in this work can be used for cyclers, we extend the scope of orbits types to higher energy cyclers and asymmetric orbits. In Barrabes and Gomez, 8,9 three-dimensional p-q resonant orbits close to periodic second species solutions (SSS) of the circular restricted three-body problem (CRTBP) were obtained. Analytical in- and out-maps ∂