Some numerical estimates of perturbation of orbital elements of artificial Earth satellite with total dynamic symmetry about rotating aspherical Earth

The problem of motion of a satellite with total dynamic symmetry about a rotating aspherical Earth was solved in an earlier study. With an accuracy to 10 to the -8th power it was possible to derive analytical formulas for perturbed Delaunay elements of a satellite orbit. It was demonstrated that the Delaunay elements characterizing the translational motion of a satellite about the Earth receive sensitive perturbations caused by the Earth's figure. The elements determining the Earth's rotational motion remain virtually constant. The formulas derived in the earlier study are used to find the numerical values of the perturbation of Delaunay elements for a specific artificial Earth satellite for a significant time period. The following case is examined: an artificial satellite of spherical configuration with perigee altitude 500 km, apogee altitude 1,000 km, longitude of ascending Omega = 45 deg, angular distance of perigee from node Omega = 30 deg, orbital inclination i = 57 deg, moment of transit through perigee tau = 0.