Integrable cases of the problem orbital evolution of satellite under the influence of planet’s oblateness the attraction of its massive satellites and the Sun

The problem combined influence of the oblateness of central planet, the attraction of its most massive (or main) satellites and the Sun on the orbital evolution of the satellite with negligible mass is considered. The evolutionary equations in planet-equatorial elements of the satellite orbit are given for arbitrary angle between the planet’s equatorial plane and the plane of its heliocentric orbit. The integrable cases of the evolutionary problem are described; the paths of its possible investigation and application to real satellite systems are outlined.