Motion of the Orbital Plane of a Satellite Due to a Secular Change of the Obliquity of its Mother Planet

Abstract

At the present state the rotational axes of Uranus and Pluto are nearly perpendicular to their orbital planes and each satellite moves in the vicinity of the equatorial plane of its mother planet. We assume that in the past a planet’s equatorial plane was nearly coincident with its orbital plane and then the inclination of the equatorial plane with respect to the orbital plane began to increase secularly. Here we discuss whether a satellite that moves in its mother’s equatorial plane continues to move in the equatorial plane or not. When the direct solar perturbation is neglected, the satellite continues to stay in the equatorial plane under the condition that the secular rate of change of the obliquity is slower than the precessional speed of the satellite orbital plane with respect to the equator.