Aaron J. Rosengren, University of California San Diego
Keywords: Cislunar Space, SSA, SDA, Astrodynamics
Abstract:
Developing and maintaining a space object catalog (SOC) for cislunar space will require significant improvements in our understanding of the way objects behave in this complicated restricted four-body problem (R4BP) environment under a realistic ephemeris model. The vast and hardly surveyable literature has instead focused on the study of the planar, circular, and restricted three-body problem (PCR3BP) or a hierarchy of more realistic, and more complicated, dynamical models, e.g., the elliptical orbit of the Moon, three-dimensional motion of the satellite, and, more recently, on the fourth-body effects from the Sun (i.e., bi-circular and restricted Hill problems, respectively designated BR4BP and RH4BP). The unquestionable merit of these simplified mathematical models cannot be overstated as they provide the underlying dynamical skeleton (i.e., the Lagrange points and their associated phase-space structures) that organizes and governs how all the possible orbital behaviors are related. The transition to a full ephemeris model, including solar and other gravitational perturbations and solar-radiation pressure (SRP), introduces additional nuances that have only been treated in piecemeal for isolated trajectories. The catalog-maintenance problem, however, requires a more holistic and global understanding of such realistic dynamics over orbital and longer timescales; a gap this work seeks to address.
We will provide a dynamical cartography of the entire cislunar “cone of shame” region (i.e., lunar exclusion zone) using an xGEO (i.e, beyond Geosynchronous) orbit parameterization applicable throughout the entire cislunar region. In general, cislunar orbits are highly perturbed by the third-body gravitational effects of the Moon and Sun. A fitting Solar-System counterpart is the Centaurs, which are a prominent group of minor bodies in highly dispersed orbits between Jupiter and Neptune. While the ubiquitous two-line element (TLE) will certainly no longer suffice, this paper, motivated by the transient multiscale dynamics of Centaurs, will showcase the overlooked utility of a piecewise (non-Keplerian) osculating element representation for the cislunar space situational/domain awareness (SSA/SDA) context. We note that the concept of geocentric elements (as physically insightful parameters) do loose their precise meaning upon entering the lunar Hill sphere, but it is at that dynamical constraint where a switch to selenocentric elements can be made.
Of the myriad of cislunar trajectories, the distant retrograde orbits (DROs) and near-rectilinear halo orbits (NRHOs) have assumed a special significance. DROs, which are stable geocentric orbits that resemble large quasi-elliptical retrograde orbits around the Moon in the rotating frame, have been proposed as parking orbits for interplanetary missions and for the unfunded Asteroid Redirect Mission. Halo orbits about L1 and L2 have been proposed for payloads supporting lunar exploration and communication, including the Lunar Gateway, as well as a parking orbit for the efficient insertion of satellites into low-Earth orbits. The NRHO of the planed Lunar Gateway, for instance, will bring the station within 3,000 km of the lunar north pole at closest approach and as far as 70,000 km over the lunar south pole. Bearing the aforementioned caveats in mind, one would expect it to have a well defined osculating set of geocentric elements for the majority of its nearly 7-day orbit. DROs, on the other hand, are expected to be generally well behaved in their entire orbital element time histories; with the exception of the vary tightly bound members of this family. 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 14-17, 2021
Track: Cislunar SSA