Efficient Formulation of the Periodic Corrections in Brouwer’s Gravity Solution

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 Lyddane’s reformulation of Brouwer’s theory.