Orbital perturbation coupling of primary oblateness and solar radiation pressure

TL;DR

This paper analyzes how solar radiation pressure couples with Earth's oblateness to influence spacecraft orbits, deriving a Hamiltonian model that identifies stable configurations and bifurcation conditions for long-term orbit maintenance.

Contribution

It introduces a Hamiltonian framework for the coupled effects of radiation pressure and oblateness, providing analytical tools for understanding and predicting stable orbit regimes.

Findings

Identification of three parameter regimes with distinct dynamical behaviors

Derivation of fixed points corresponding to frozen orbits

Analytical expressions for bifurcation lines separating regimes

Abstract

Solar radiation pressure can have a substantial long-term effect on the orbits of high area-to-mass ratio spacecraft, such as solar sails. We present a study of the coupling between radiation pressure and the gravitational perturbation due to polar flattening. Removing the short-period terms via perturbation theory yields a time-dependent two-degree-of-freedom Hamiltonian, depending on one physical and one dynamical parameter. While the reduced model is non-integrable in general, assuming coplanar orbits (i.e., both Spacecraft and Sun on the equator) results in an integrable invariant manifold. We discuss the qualitative features of the coplanar dynamics, and find three regions of the parameters space characterized by different regimes of the reduced flow. For each regime, we identify the fixed points and their character. The fixed points represent frozen orbits, configurations for which the long-term perturbations cancel out to the order of the theory. They are advantageous from the point of view of station keeping, allowing the orbit to be maintained with minimal propellant consumption. We complement existing studies of the coplanar dynamics with a more rigorous treatment, deriving the generating function of the canonical transformation that underpins the use of averaged equations. Furthermore, we obtain an analytical expression for the bifurcation lines that separate the regions with different qualitative flow.