An investigation on space debris of unknown origin using proper elements and neural networks, Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics

Abstract

An investigation on space debris of unknown origin using proper elements and neural networks Proper elements represent a dynamical fingerprint of an object’s inherent state and have been used by small-body taxonomists in characterizing asteroid families. Being linked to the underlying dynamical structure of orbits, Celletti, Pucacco, and Vartolomei have recently adopted these innate orbital parameters for the association of debris from breakup or collision into its parent satellite. Building from this rich astronomical heritage and recent foundations, we introduce an unsupervised learning method—density-based spatial clustering of applications with noise (DBSCAN)—to determine clusters of orbital debris in the space of proper elements. Data is taken from the space-object catalog of trackable Earth-orbiting objects in the form of two-line element sets. Proper elements for debris fragments in low-Earth orbit are computed using an ad hoc numerical scheme, akin to the state-of-the-art Fourier-series-based synthetic method for the asteroid domain. Given the heuristic nature of classical DBSCAN, we investigate the use of neural networks, trained on known families, to augment DBSCAN into a classification problem and apply it to analyst objects of unknown origin. Theory and applications of fast Lyapunov indicators to model problems of celestial mechanics In the last decades, we have seen a rapid increment in the use of finite-time chaos indicators in celestial mechanics. They have been used to analyze the complex dynamics of planetary systems, of minor planets and of space debris. In fact, theoretical studies on fundamental dynamical models have revealed that, computed on short time intervals, they allow to efficiently detect resonances, represent the phase portraits of complex dynamics, compute center-stable-unstable manifolds as well as Lagrangian coherent structures. In this seminar, we focus on applications of the fast Lyapunov indicator (FLI) and review through examples why its computation is particularly powerful for those systems whose solutions may have an asymptotic behavior very different from the short-term one, as it is the case of sequences of close encounters in gravitational systems and the advection of particles in aperiodic flows. The main case study which is considered is the computation of the manifold tubes and the related transit orbits in the restricted three-body problem.