Reformulation of the Brouwer geopotential theory for improved computational efficiency

Abstract

The theory, as derived by Brouwer and later modified by Lyddane, of the motion of an artificial Earth satellite perturbed by the first five zonal harmonics is reformulated in terms of an alternate set of variables. This alternate set of variables produces an equivalent solution, has no small eccentricity or small inclination restrictions, and allows calculation of position and velocity with considerably fewer algebraic and trigonometric operations. In addition, the alternate set of variables avoids one solution of Kepler's equation.