With what sort of gravitation are Saturn's Rings held together? It is very spectacular and intriguing compared to the way Earth's gravitation acts.
I do not have a basic or conceptual idea of what/how motion happens in the Rings. What makes water/ice matter to be confined to the equatorial planes and yet be bound within so many individual Rings? Does inverse square law operate on the icy plate orbiting matter in a force field ? Is there a mathematical model of relative motion of individual glacier sort of ice-block stone masses orbiting inside of the flat planetary Rings?
Has an ordinary differential equation been written for dynamic motion of particles in the Rings?
A purely conceptual model is written to include strong precession. Here each particle has radial velocity along with circumferential and is bound between extreme radii. Wish to see such Ring orbits theoretically derived like Kepler/Newton planetary orbits of Earth satellites considering conservation of momentum, net forces acting as a function of radius and the Inverse squared law of gravitational attraction that operates universally.
Is a particle forever confined to a Ring ? Are there no Kepler type laws or rules for Saturn? Is there an elementary method to verify calculate/ correlate observed and calculated time period of some Ring particles and some moons in most simple cases? ( For time being we leave out the moon darting across some Rings and such advanced situations.) I hope to gain clarity about satellite particle fundamentals.Please point out references about same.