Bifurcations of lunisolar secular resonances for space debris orbits

TL;DR

This paper uses bifurcation theory to analyze how lunisolar secular resonances affect space debris orbits, focusing on inclination-dependent resonances and their bifurcations, to identify stable and unstable orbital regions.

Contribution

It introduces a Hamiltonian model for inclination-dependent lunisolar resonances and applies bifurcation theory to determine energy thresholds for resonance bifurcations in space debris dynamics.

Findings

Identified energy thresholds for bifurcations of secular resonances.

Mapped stable and unstable regions in phase space.

Provided insights into inclination-dependent resonance phenomena.

Abstract

Using bifurcation theory, we study the secular resonances induced by the Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depend only on the debris' orbital inclination. This class is typically subdivided into three distinct types of secular resonances: those occurring at the critical inclination, those corresponding to polar orbits, and a third type resulting from a linear combination of the rates of variation of the argument of perigee and the longitude of the ascending node. The model describing the dynamics of space debris includes the effects of the geopotential, as well as the Sun's and Moon's attractions, and it is defined in terms of suitable action-angle variables. We consider the system averaged over both the mean anomaly of the debris and those of the Sun and Moon. Such multiply-averaged Hamiltonian is used to study the lunisolar resonances which depend just on the inclination. Borrowing the technique from the theory of bifurcations of Hamiltonian normal forms, we study the birth of periodic orbits and we determine the energy thresholds at which the bifurcations of lunisolar secular resonances take place. This approach gives us physically relevant information on the existence and location of the equilibria, which help us to identify stable and unstable regions in the phase space. Besides their physical interest, the study of inclination dependent resonances offers interesting insights from the dynamical point of view, since it sheds light on different phenomena related to bifurcation theory.