Local and Global Dynamical Portraits of Cislunar xGEO Space

Aaron Rosengren (University of California, San Diego)

Mercredi 28 juin, 11h00, salle Coriolis (Galois).

Abstract. The nonlinear astrodynamics in the cislunar space beyond the geosynchronous belt (xGEO), encompassing secular, resonant, chaotic, close-encounter, and manifold dynamics, is dramatically different than the weakly perturbed Keplerian approach used for over a half century for the detection and tracking of objects near Earth. In contrast to the traditional geocentric domains, the predominant resonances in xGEO are governed by octupolar and higher-order perturbations to the classical Kozai-Lidov-von Zeipel dynamics, among, hitherto, unstudied interactions with the lunar orbital and precession frequencies. Furthermore, while mean-motion resonances (MMRs) constitute one of the most important and far-reaching aspects of dynamical astronomy, they have remained woefully underrated in circumterrestrial dynamics, in part because the orbits of most satellites thus far are too low to be affected by mean-motion commensurabilities. Using detailed Hamiltonian-perturbation theory, grounded in astronomical insight and heritage, we uncover the nonlinear lunisolar secular resonances and lunar MMRs that significantly affect the structure of xGEO phase space. The orbital architecture of current and historic xGEO space objects differ markedly from the classical problems presented by nature (e.g., dominant forces, relevant timescales, hierarchical configurations, etc.), rendering many of the time-honored methods of Solar-System dynamics inapplicable. In this talk, we will showcase the inherent limitations of the perturbed two-body approach and highlight how the local picture can be complemented with the global geometric dynamical portrait provided by semi-analytical approaches to the restricted three-body problem. Aspects of this research have been done in collaboration with Shane D. Ross of Virginia Tech.