A semianalytical satellite theory for weak time-dependent perturbations

The modifications of the semianalytical satellite theory required to include these 'weak' time dependent perturbations are described. The new formulation results in additional terms in the short periodic variations but does not change the averaged equations of motion. Thus the m monthly terms are still included in the averaged equations of motion. This contrasts with the usual approach for the strongly time dependent perturbations in which the m monthly (or m daily, if tesseral harmonics are being considered) terms would be eliminated from the averaged equations of motion and included in the short periodics computation. Numerical test results for the GPS case obtained with a numerical averaging implementation of the new theory demonstrate the accuracy improvement.