Dynamic orbit propagation in a gravitational field of an inhomogeneous attractive body using the Lagrange coefficients

The analytical methods have nearly been replaced by the numerical methods due to their higher accuracy and accessibility of computation facilities. The semi-analytical Lagrange method of orbit propagation using f and g series is a competitive alternative to the numerical integration technique if the Lagrange coefficients are derived in a full gravitational field. In this paper, a generalization of the Lagrange method of orbit propagation is introduced. In other words, we introduce a complete form of the Lagrange coefficients in all force fields developed in the spherical harmonics for example full gravitational field of the Earth. The method is numerically compared with the numerical integration technique. In order to show the numerical performance of the method, it has been implemented for orbit propagation of a GPS-like MEO and CHAMP-like LEO satellites. Discrepancy at centimeter level for CHAMP-like and sub-millimeter accuracy for GPS-like satellites shows relatively high performance of the developed algorithm. Compared to integration method, the proposed Lagrange method is nearly faster by a factor two for small Nmax and four for large Nmax.