Dynamical models and the onset of chaos in space debris

TL;DR

This review explores mathematical models and analytical methods used to understand the complex dynamics and chaos onset in space debris orbits, considering various forces and resonances affecting debris at different altitudes.

Contribution

It systematically compares different formalism approaches and analyzes the conditions leading to chaos in space debris dynamics, including resonance overlap and secular effects.

Findings

Resonance overlap can induce chaos in space debris trajectories.

Large area-to-mass ratios significantly influence debris stability.

Lunisolar secular resonances contribute to chaotic behavior.

Abstract

The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. Such models and methods strongly depend on the altitude of the objects above Earth's surface, since the strength of the different forces acting on an Earth orbiting object (geopotential, atmospheric drag, lunar and solar attractions, solar radiation pressure, etc.) varies with the altitude of the debris. In this review, our focus is on presenting different analytical and numerical approaches employed in modern studies of the space debris problem. We start by considering a model including the geopotential, solar and lunar gravitational forces and the solar radiation pressure. We summarize the equations of motion using different formalisms: Cartesian coordinates, Hamiltonian formulation using Delaunay and epicyclic variables, Milankovitch elements. Some of these methods lead in a straightforward way to the analysis of resonant motions. In particular, we review results found recently about the dynamics near tesseral, secular and semi-secular resonances. As an application of the above methods, we proceed to analyze a timely subject namely the possible causes for the onset of chaos in space debris dynamics. Precisely, we discuss the phenomenon of overlapping of resonances, the effect of a large area-to-mass ratio, the influence of lunisolar secular resonances. We conclude with a short discussion about the effect of the dissipation due to the atmospheric drag and we provide a list of minor effects, which could influence the dynamics of space debris.