On the 'thickness' of Saturn's rings caused by satellite and solar perturbations and by planetary precession

In the present paper, long-period and secular variations of the longitude of ascending node are derived for a particle orbiting an oblate precessing planet subjected to perturbation by an exterior satellite moving along a low-inclination orbit. It is shown that precession of Saturn under the solar torque, which causes the Laplace plane to be noninertial, is also effective in producing a forced inclination. The height above the Laplace plane associated with this variation is several meters for a particle located in the middle of the ring.