An analytical method od determination of luni-solat perturbations of the satellite motion is described here. The motion of perturbing body is described by trigonometrical series with the necessary accuracy. The determination of perturbations is made by numerous analytical transformations of the series by means of computer. As a result of these transformations the original accuracy is lost because of the limitation of the number of terms in series. The loss of accuracy is subjected to analysis by means of numerical tests and intotal accuracy of original series is estimated for fixed required accuracy of the calcualtion of satellite coordinates.
Merits of an analytical theory of the satellite motion in comparison with numerical integration for applications to problems of geodynamics and satellite geodesy are discussed. Urgent need of further advance of modern theories is proved. A method is described of the development of an analytical theory by means of integration in the first and second orders of differential equations for elements of E. P. Aksenov intermediate orbit. The Earth´s oblateness is fully taken into account in the intermediate orbit. The theory takes into account combined perturbations with respect to different perturbing factors. The appropriate computer algorithm for the obtention of the perturbations is offered. A comparison of the theory with the results of numerical integration is made for the case of perturbations caused by the terrestrial gravitational field. The comparison shows that the accuracy of the new theory turns out to be no worse that 18 in satellite coordinates.