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

Long-period and secular variations of the inclination and of the longitude of ascending node are derived for a particle orbiting an oblate, precessing planet, while under perturbation by an exterior satellite on a low inclination orbit. The variations are found to zeroth order in e and first order in i by using a two-timescale technique; they are obtained in closed form and are written relative to the mean ring plane, the Laplace or proper plane. If the planetary precession is ignored, satellite perturbations, when coupled with the effects of oblateness, induce a forced motion in which the line of nodes precesses uniformly at rate 2n/sub j/ whereas the orbital inclination is ω/sub J/sini/sub j//(ω/sub F/+2n/sub j/), where n/sub j/ is the mean motion of the jth satellite, ω/sub J/ is the orbit plane's precession rate caused by the jth satellite, and ω/sub F/ is the precession rate produced by the planet's oblateness. Typical amplitudes of these satellite-induced perturbations from highest to lowest distance off the equatorial plane, when measured at 105 km from the planet, are 0.1 m, 0.3 m, and 2 m due to Mimas, Tethys, and Titan, respectively; the other satellites cause much smaller variations. The character of the solar perturbation is like that due to a satellite but it produces a typical amplitude of 9 m. For each of these perturbers, the amplitude varies by aboutabout an order of magnitude from the inner to the outer edge of the ring, owing to the radial dependence of ω/sub J/ and ω/sub F/