Three-dimensional perturbations of particles in a narrow planetary ring
The complex form of Saturn's F ring is presently addressed through a numerical modeling of short-term 3D narrow-ring dynamics with the Gauss perturbation equations. The distance of closest approach, which determines the strength of interaction, is noted to depend on orbital orientation as well as on orbital eccentricity and the semimajor-axis separation of the ring particle from the perturbing satellite. Perturbations to substantial inclinations through the appropriate choice of parameters are illustrated by simulations of a narrow ring initially consisting of three strands of 800 particles each, and it is demonstrated that the modest, out-of-plane satellite-induced vertical and horizontal distortions of three narrow bands generate a structure akin to the 'braided' F-ring.