We suggest an advanced algorithm for semi-analytical calculation of orbital perturbations of Earth artificial satellites caused by the gravity attraction of the “3rd-bodies” (the Moon, the Sun, major planets). A new accurate analytical series for the relevant perturbation function is developed. It is obtained through a careful spectral analysis of the long-term DE406 planetary/lunar ephemerides and valid over 2000 years, 1000-3000. The series is used in the author’s semi-analytical model of satellite motion. The results of the motion prediction of several Earth satellites obtained by means of the semi-analytical model and a numerical integration method are compared.
