The generalized F and G series for the satellite orbit propagation

Abstract

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