# Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

## TL;DR

This paper develops an analytical model to analyze the equilibrium points and phase space of satellite dynamics influenced by planetary oblateness and solar radiation pressure, aiding understanding of orbital stability.

## Contribution

It introduces a novel analytical framework combining planetary oblateness and solar radiation effects in a phase space model for satellite dynamics.

## Key findings

- Derived equilibrium points and stability conditions in eccentricity-resonant angle space.
- Provided Hamiltonian formulation for the coupled effects.
- Applied model to Earth's case with visualization tools.

## Abstract

The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure perturbations. A two-dimensional differential system is derived by considering the classical theory, supported by the existence of an integral of motion comprising semi-major axis, eccentricity and inclination. Under the single resonance hypothesis, the analytical expressions for the equilibrium points in the eccentricity-resonant angle space are provided, together with the corresponding linear stability. The Hamiltonian formulation is also given. The model is applied considering, as example, the Earth as major oblate body, and a simple tool to visualize the structure of the phase space is presented. Finally, some considerations on the possible use and development of the proposed model are drawn.