The satellite version of the restricted three-body problem formulated on the basis of classical Gylden-Meshcherskii problem is considered. Motion of the point P_2 of infinitesimal mass about the point P_0 is described in the first approximation in terms of the osculating elements of the aperiodic quasi-conical motion, and an influence of the point P_1 gravity on this motion is analyzed. Long-term evolution of the orbital elements is determined by the differential equations written in the Hill approximation and averaged over the mean anomalies of points P_1 and P_2. Integrability of the evolutionary equations is analyzed, and the laws of mass variation have been found for which the evolutionary equations are integrable. All relevant symbolic calculations and visualizations are done with the computer algebra system Mathematica.
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