RSO proper elements: Concept, methods, and application to maneuver detection

Abstract

Asteroid families consist of swarms of fragments generated after energetic interasteroidal collisions in the distant past that resulted in the breakup of their progenitors. They are recognized by searching for clusters in the three-dimensional space of “proper elements”; parameters characterizing the asteroid orbits that are very close to fundamental invariants of motion, and thus keep a dynamical record of the initial proximity of the orbits generated by a catastrophic fragmentation event. In the circumterrestrial context, proper elements have recently been applied to the dynamical taxonomy of resident space objects (RSO) for the association of debris from breakup into its “parent” satellite. Here, we clarify, adapt, and extend this fundamental concept to space situational awareness for on-orbit maneuver/anomaly detection. RSO proper elements, being linked to the underlying dynamical structure of orbits, can provide a more robust metric within existing maneuver-detection algorithms, through assessment of the induced changes in these quasi invariants of the motion. We highlight the deeper connection of proper elements to classical frozen orbits in Earth-satellite dynamics and to secular elements in artificial satellite theories based on canonical perturbation theory and showcase several techniques for their numerical computation, including a newly proposed Ptolemy method; applicable to both the asteroid and space-debris domains. We apply a Bayesian online changepoint-detection (BOCD) algorithm in both mean- and proper-element space and compare their performances for orbit-maneuver detection.