CONSTRUCTION OF PERIODICALLY EVOLVING ORBITS OF A SATELLITE OF AN OBLATE PLANET IN THE AVERAGED HILLS PROBLEM WITH ALLOWANCE FOR PRECESSIONOF THE ORBIT OF A PERTURBING POINT

Our goal is to find special orbits whose elements vary with the same p eriod due to perturbations. In the averaged Hill's problem with an obl ate central planet, we constructed examples of such periodically evolv ing orbits for the satellite-oblate Earth-Moon-Sun system in the model of an elliptical lunar orbit that precesses with a constant inclinati on i(1) to the plane of the ecliptic. Based on generating orbits (i(1) = 0), we obtained periodic solutions of an evolving system with a per iod that is a multiple of the precession period of the lunar orbit for i(1) = 5 degrees.15.15 using the numerical solution of a two-dimensio nal boundary-value problem. Our numerical results are confirmed by the calculations performed by an independent numerical-analytical method.