Solar radiation pressure perturbations for Earth satellites II. an approximate method to model penumbra transitions and their long-term orbital effects on LAGEOS

We have developed an approximate version of our theory (Vokrouhlicky et al. 1993c) for the perturbing force due to solar radiation pressure undergone by artificial Earth satellites when they cross the penumbra zones. The relative discrepancies in the instantaneous acceleration values with respect to the complete theory are generally smaller than 1%, and no systematic pattern resulting into spurious long-term perturbations arises. At the same time, the approximate approach leads to a considerable gain in the computing time needed for evaluating the perturbing force, typically an improvement by a factor 10 to 50. As a consequence, the theory is now suitable for implementation in the orbit analysis/determination codes used in space geodesy