Efficient formulation of the periodic corrections in Brouwer's gravity solution

TL;DR

This paper presents a simplified, nonsingular formulation of Brouwer's gravity solution's periodic corrections, making it applicable to a wider range of orbital eccentricities and inclinations while maintaining the benefits of action-angle variables.

Contribution

The authors introduce a new nonsingular variable set for Brouwer's solution that simplifies periodic corrections and extends their validity to all eccentricities below one and most inclinations.

Findings

Periodic corrections are valid for any eccentricity below one.

The new formulation is significantly simpler than previous nonsingular corrections.

The approach retains all benefits of the action-angle variables.

Abstract

The periodic terms of Brouwer's gravity solution are reconstructed in a nonsingular set of variables which are derived from the well-known polar-nodal variables. This change does not affect the essence of the solution, which still keeps all the benefits of the action-angle variables approach, and yields two major improvements. Namely, the periodic corrections of Brouwer's solution are now valid for any eccentricity below one and any inclination except the critical inclination, and, besides, are significantly simpler than the nonsingular corrections in Lydanne's reformulation of Brouwer's theory.