Aaron J. Rosengren, University of California San Diego; Shane D. Ross, Virginia Tech; Bhanu Kumar, Jet Propulsion Laboratory, Caltech; Anjali Rawat, Virginia Tech
Keywords: Cislunar SSA, Astrodynamics, Space Situational/Domain Awareness (SSA/SDA), Restricted Three-Body Problem, Perturbed Two-Body Problem
Abstract:
A rigorous dynamical definition for xGEO is the critical distance at which the secular contributions from the 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 dynamics in this domain. A many-sided and detailed investigation of the resonant structure of xGEO space, aside from its own particular significance, is of prime importance for space domain awareness (SDA) beyond GEO as such resonances significantly affect the global structure of orbital phase space. In contrast to the traditional LEO-to-GEO domain, the predominant resonances in xGEO are governed by octupolar perturbations to the classical von Zeipel-Lidov–Kozai dynamics, among, hitherto, unstudied interactions with the lunar orbital and precession frequencies. While mean-motion commensurabilities (of orbital periods) constitute one of the most important and far-reaching aspects of dynamical astronomy, they have remained woefully underrated in Earth-satellite dynamics in part because the orbits of most satellites thus far are too low to be affected by mean-motion resonances (MMRs). “What are the Kirkwood gaps of cislunar space?” is a question of great current interest for mission planners as we are locating our space-based assets, such as the IBEX and TESS, in predominant lunar MMRs that have hitherto only been treated in piecemeal. Also of special note is ESA’s SMART-1 low-thrust spiraling trajectory to the Moon, which used a combination of multiple coast arcs and weak lunar gravity assists on account of passage through lunar MMRs. However, the manifolds emanating from unstable first-order MMRs, which can enable rapid natural dynamical transfers, have been largely underappreciated and unexplored.
Cislunar space, outside the confines of near-Earth satellite orbits, 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. It is precisely the distinctive and multi-faceted dynamical features of this regime that complicates SDA efforts and represents significant challenges for space sustainability. This investigation will combine the local picture provided by the perturbed-Hamiltonian formulation of xGEO astrodynamics 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. Such a holistic dynamical mapping of cislunar space will not only ensure that future xGEO satellites will have predictable behaviors over both the nominal (and possibly extended) mission timescales (if warranted), thus avoiding an IBEX-like situation, but that the satellites and their rocket bodies will eventually meet their demise through atmospheric reentry (without the need to make future significant orbital adjustments, a la ESA’s INTEGRAL mission.
Furthermore, the insights and constraints from Hamiltonian mechanics can aid in detection and tracking amidst this new dynamic topography. 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. We will provide a framework to represent the dynamical sensitivity of various regimes in terms of intuitive orbit parameters and detail how they can be used to identify relevant metrics for surveillance design strategies (e.g., search and revisit rates, accuracy, surveillance volume).
Date of Conference: September 17-20, 2024
Track: Cislunar SDA