The generalized F and G series for the satellite orbit propagation

In this paper, an advanced version of the Lagrange method, F and G series, is proposed for the many applications in the celestial mechanics and space science such as initial orbit determination and satellite orbit propagation. In this development, the Lagrange coefficients were developed from a gravitational field of an inhomogeneous attractive body to all the perturbing accelerations acting on an orbiter. The efficiency of the method is tested for the satellite orbit propagation. This assessment is based on the comparison between the Lagrange solution and the analytical one for Keplerian motion and numerically integrated orbit for non-Keplerian motion. The discrepancy at centimeter and sub-centimeter accuracy shows the performance of the developed algorithm for MEO and LEO satellites orbit propagation. The results of computational time showed that the Lagrange method is as time-consuming as the multi-step methods where it is faster than the single-step methods. Besides the CPU-time, the stability test of the Lagrange method shows that it is as stable as the single-step and is more stable than the multi-step methods at the equivalent orders. Therefore, the Lagrange method offers the advantages of the single- and multi-step methods.