New Dynamical Connections Between Circumterrestrial Space Objects and Small Solar System Bodies

Under the Newtonian laws of motion and gravitation, there is little distinction between astrodynamics and celestial mechanics. With the rise of the space industry in the 21st century, the emerging field of astrodynamics, focusing on the space-engineering aspects of dynamical astronomy, was mainly concerned with designing spacecraft trajectories and studying circumterrestrial satellite orbits with minute detail. This time period also ushered in a new era for celestial mechanics, with the advent of sophisticated computers and new qualitative approaches in dynamical systems theory, permitting explorations of the long-term dynamical evolution and stability of small Solar-System bodies. Despite a common astronomical heritage, these two subfields of space engineering and space science have progressed along somewhat independent utilitarian lines with little cross-fertilization of theoretical methods and computational techniques. But in recent years, astrodynamics has had to face new problems concerning the long-term motion of space debris. The intrinsic similarities between these remnants of past missions, satellite explosions, and collisions and the remnants of Solar-System formation (e.g., asteroids, comets, Centaurs, Kuiper-belt objects) are ubiquitous. Asteroid families, for example, are formed when an asteroid is disrupted in an energetic interasteroidal collision, the members of the family thus being pieces of the original asteroid. In the same vein, the majority of space debris result from satellite fragmentation events due to on-orbit explosions or hypervelocity impacts (e.g., unintentional collisions among satellites and space debris or deliberate anti-satellite tests). Moreover, the profound insights of Hamiltonian dynamical systems theory have revolutionized the design of spacecraft trajectories, and have contributed to the development of new space-based astronomical observatories (e.g., NASA's James Webb Space Telescope) that have transformed our understanding of the cosmos. The space-manifold dynamics that enable a grand tour of the Solar System through the `Interplanetary Transport Network' may also drive the short-term capture and transit of comets and asteroids on rapid timescales, hitherto unexplored in the planetary-dynamics context. This dissertation explores these dynamical connections in detail, with a focus on the multi-timescale dynamics of circumterrestrial space objects and small Solar-System bodies, and bridges the dynamical gaps that exist in studies concerning the long-term and short-term evolution of these artificial and natural celestial bodies. As near-Earth space gets more and more congested, contested, and competitive, a rigorous classification scheme based upon scientific taxonomy is needed to properly identify, group, and discriminate resident space objects (RSOs). With over 1,000 active satellites currently on orbit, and significantly more planned for satellite mega-constellations (e.g., SpaceX's Starlink, OneWeb, Amazon's Kuiper) and cislunar space, the problems of taxonomy and orbital event detection are both persistent and relevant for space situational awareness (SSA). This dissertation adapts and extends a concept from small-body taxonomists used in characterizing asteroid families known as proper elements. These represent a dynamical fingerprint of the object’s inherent state and provide a unique criterion that is otherwise lacking. But these innate orbital parameters have not been adequately explored in the geocentric domain, in part, because the traditional orbits of artificial Earth satellites and space debris, and their dynamical environments, differ so markedly from the classical problems presented by nature (e.g., dominant forces, relevant time scales, etc.). This fact renders many of the time-honored methods of Solar-System dynamics inapplicable for near-Earth space (Chapter 1) and necessitate the development of new rigorous and non-conventional approaches. This dissertation works out the theory of proper orbital elements in the circumterrestrial context, linking them to classical frozen orbits and to secular elements in the artificial satellite theories of our forebears, and showcases several analytical, semi-analytical, and numerical techniques for their computation. We develop a new generalized computational approach --- the Ptolemy-epicyclic method (Chapter 2) --- based on the topology of perturbed Keplerian orbits, which is applicable to both asteroid and RSO dynamics. We show that proper elements, being linked to the underlying dynamical structure of orbits, provide a more robust metric within these existing maneuver-detection algorithms, through assessment of the induced changes in these quasi invariants of the motion (Chapter 3). We then show that these unique orbital signatures can be applied to the dynamical taxonomy of RSOs and the association of debris from breakup into its ``parent'' satellite (Chapter 4), adopting a Bayesian online changepoint-detection (BOCD) algorithm for on-orbit maneuver/anomaly detection and incorporating deep learning into clustering methods for space-debris family characterization (Chapter 5). This dissertation then turns its attention to the underappreciated and unexplored short-timescale dynamics of space manifolds in celestial mechanics. Centaurs are a prominent group of small Solar-System bodies in highly dispersed orbits between the two main belts. They are a short-lived transient phase connecting their source reservoir in the Kuiper Belt to the Jupiter-family comets (JFCs) and Halley-type comets (HTCs), but the precise dynamical hand-off process between the Centaurs and these short-period comet (SPC) populations remains unclear. The recent finding of an orbital gateway between Jupiter and Saturn, funneling Centaurs into the inner Solar System, has cast some light on the orbital migration of these enigmatic bodies. Yet, no dynamical mechanism to explain the existence of this apparent conduit has hitherto been offered. This dissertation links seminal research conducted over two decades ago on Jovian-induced space manifolds with a new understanding of the orbital architecture of these gravitational structures to elucidate the nature of this and other dynamical channels for the rapid transport of small bodies (Chapter 6). We study the global impact of space-manifold dynamics on the current, past, and future states of the observed SPCs and Centaurs, revealing the surprising depth to which the space-manifolds emanating from the neighborhood of Jupiter can permeate the outer Solar System, having an exuberant and profound control on these distant orbital regimes. This dissertation combines the well-developed techniques of astrodynamics for the study of space manifolds with the modern analytical and numerical tools of planetary dynamics, harnessing these in unique ways to probe for the first time the high time-resolution details of the strongly chaotic evolutions of planet-crossing small bodies of the outer Solar System