PhD Seminar Series: “Dynamical Frameworks for Tracking and Sustaining Space Operations in Cislunar xGEO”

Abstract: 

Cislunar space, outside the confines of the geosynchronous belt (xGEO), is poised to serve as a new high ground for space operations, and, like its circumterrestrial counterpart, must be sustained against risk from debris and other threats. A rigorous dynamical definition for xGEO is the critical distance at which the secular contributions from lunisolar perturbations exceed those from Earth oblateness, known in astronomical parlance as the Laplace radius. xGEO fundamentally represents a restricted four-body problem (R4BP), which can be approached locally using the perturbed-Hamiltonian formulation or globally using techniques stemming from the R3BP. Remote sensing, regardless of the phenomenology, must accommodate the complex multi-body astrodynamics in this domain, which is dramatically different from 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. Lunar mean-motion resonances (MMRS) significantly shape cislunar dynamics forming stable-unstable pairs, with corresponding intermingled chaotic and regular regions. The region of influence of the unstable resonant orbits (also called the chaotic resonance zone) can be rigorously defined using the separatrix of unstable resonant periodic orbits surrounding stable quasi-periodic regions (forming the stable resonance width). Furthermore, the manifolds emanating from unstable MMRs can enable rapid dynamical transfers between resonances through heteroclinic connections.  

This study combines the local picture provided by the perturbed-Hamiltonian formulation with the global geometric dynamical portrait provided by semi-analytical, dynamical-systems theory approaches to the restricted three-body problem, harnessing these in unique ways to probe for the first time the high time-resolution details of the strongly chaotic orbital evolution of all distant cislunar space probes. Furthermore, the insights and constraints from Hamiltonian mechanics can aid in detection and tracking amidst this new dynamic topography. In this talk, we will show how these investigations can enable observers to decide where and when data should be obtained in future campaigns, for example, by providing stringent constraints through stability analysis of the existing and predicted orbits. 

Aspects of this research have been done in collaboration with Shane D. Ross and Anjali Rawat of Virginia Tech and Bhanu Kumar of the University of Michigan.