Peculiarities of secular orbital evolution of hypothetical Uranus’s satellites

A problem is considered on secular perturbations of negligible mass probe satellite’s orbit caused by joint influence of central planet’s oblateness and attraction of its most massive (or main) satellites and the Sun. Unlike previous researches of this problem analytical expression of complete averaged perturbing function is got for the arbitrary inclination of probe satellite’s orbit. A numerical method is used for solving of the evolutional system with arbitrary values of constant parameters and initial elements. The behavior of a certain number of orbits is studied for the satellite system of Uranus on time intervals about tens of thousands years in area of approximately equal influence of the considered perturbing factors. The main role of Lidov–Kozai effect is revealed for qualitative explanation of absence of small bodies on almost circular near equatorial orbits with semi-major axes exceeding an approximately 1.8 million km.