Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations

TL;DR

This paper develops an analytical model of the coupled effects of solar radiation pressure and planetary oblateness on satellite orbits, enabling simplified mission design and deorbiting strategies through dynamical systems analysis.

Contribution

It provides a detailed derivation of resonant dynamics near orbital resonances, including bifurcation analysis and an analytical formula for satellite deorbiting conditions.

Findings

Resonant interactions significantly influence orbital evolution.

Analytical expressions for invariant manifolds are derived.

A simple formula for deorbiting area-to-mass ratio is provided.

Abstract

Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun--Earth line. Resonant interactions lead to non-trivial orbital evolution that can be exploited in mission design. Moreover, the dynamics in the vicinity of each resonance can be analytically described by a resonant model that provides the location of the central and hyperbolic invariant manifolds which drive the phase space evolution. The classical tools of the dynamical systems theory can be applied to perform a preliminary mission analysis for practical applications. On this basis, in this work we provide a detailed derivation of the resonant dynamics, also in non-singular variables, and discuss its properties, by studying the main bifurcation phenomena associated to each resonance. Last, the analytical model will provide a simple analytical expression to obtain the area-to-mass ratio required for a satellite to deorbit from a given altitude in a feasible timescale.