Prediction of artificial satellite positions on the basis of the second order theory of motion

Some contemporary solutions of an artificial satellite orbital motion need analytical theories on a high level of accuracy. For example, the application of the analytical methods (general perturbations) becomes advantageous when a large number of satellite orbits have to be predicted simultaneously. Since the general perturbations method usually uses mean orbital elements as arguments, while the osculating elements play the role of initial conditions for predictions, the relation between the osculating and mean elements has to be determined on the same level of accuracy as that of the theory of motion applied. The paper presents a new relation between osculating and mean orbital elements based on the Mersman (1970) algorithm for the Hori-Lie perturbation method. The inverse transformation from the osculating into mean elements has the same general form as the direct transformation from the mean into osculating elements. Different are the signs of the generator in the transformations. The two kinds of transformations are realized with the same accuracy. The theory of motion includes all terms of the second order of the short- and the long-period perturbations due to zonal and tesseral harmonics of an arbitrary degree and order. Secular perturbations are included on an appropriate level of accuracy. The formulas for perturbations are based on the generalized lumped coefficients and have relatively compact forms. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.