Any satellite moving in the real gravitational field of the central planet is affected by some forces due to rotati- onal motion of the main planet-fixed coordinate system. For the Earth such a system is the Terrestrial Reference System (TRS) conventionally defined by the coordinates of some terrestrial sites. The coefficients of the Earth potential expansion are assumed to be constants there, but to correctly calculate the perturbations of satellite motion due to the geopotential one should take into account the well-known effects of polar motion, of Earth irregular rotation, of nutation and of precession of the geoequator. There are some analytical methods allowing to take into account some of these effects (e.g., Y.Kozai \& H.Kino- shita, Celest. Mech.,7, 1973), but no one of them known to the author can be used to do that uniformly for any rotation of the TRS. Also, the accuracy of these methods does not satisfy all the time to the current level of experiments in the space and to accuracy of modern tracking data.
The presentation describes a new approach in this field. Earlier, B.Jeffreys (Geophys. J.,10, 1965) obtained an exp- ression for transformation of elementary spherical functions under rotation through three Euler angles. Using the results of that job we expressed the gravity coefficients of the pla- netary potential expansion in different rotated coordinate systems as functions of the standard set of the coefficients determined in the body-fixed system and of the angle and of the direction of a rotation (S. Kudryavtsev, Celest. Mech., submitted). The formulas are finite and exact, and they are valid for any value of rotation angle.
The case of small rotations was specially investigated. The trigonometric functions contained in the formulas were res- tricted up to and including the second order of the argument, and simplified dependencies which are more suitable for prac- tical calculations were obtained. All the transformations from the TRS to the inertial reference frame of the mean equinox and equator of epoch J2000 were considered. Among them there are two rotations for polar motion, two rotations for the uniform and irregular parts of Earth rotation, two rotations for nuta- tion and three rotations for precession. The final expressions for the gravity coefficients in the inertial reference system J2000 as functions of the set of the standard gravity coeffici- ents determined in the TRS and of nine rotation angles (where eight of them are small) were found. It was proved that the expressions are valid over an interval of time of more than 100 years for all of the rotations due to precession and prac- tically infinite time - for other considered rotations.
By substituting the gravity coefficients expressed in the J2000 to the analytical theory of satellite motion which is being developed by the author we can uniformly calculate and investigate each of the effects of polar motion, of nutation and of precession on Earth satellite motion.