On the evolution of satellite orbits under the action of the planet’s oblateness and attraction by its massive satellites and the sun

The problem of the joint influence of the oblateness of a central planet and attraction by its most massive (or main) satellites and the Sun on the orbital evolution of a satellite with a negligible mass is considered. For an arbitrary angle between the equatorial plane of the planet and the plane of its heliocentric orbit, the evolution equations have been derived in the planeto-equatorial elements of the satellite orbit. Integrable cases of the evolution problem are described. The influence of Uranus’s main satellites on the orbital evolution of its real and hypothetical satellites has been revealed through numerical calculations and analytical estimations.