Аннотация:Relativistic equations of motion of the earth's satellite in the harmonic nonrotating geocentric coordinate system are presented. In the relativistic parts of the equations, the Schwarzschild, Lense-Thirring, and quadrupole perturbations from the earth as well as tidal perturbations from the sun and moon are taken into account. The equations are derived by transforming the satellite's equations of motion from the barycentric coordinate system to the geocentric one, and by directly applying the geodesic principle in the geocentric coordinate system.