Contribution of Magnetism to the Origin of Saturn's Rings

In this paper, we derive the magnetization relationships for magnetically uniform spherical particles of Saturn's rings, and solve the problem of a solitary magnetized sphere and a spherical particle among identical particles scattered in a disk-like structure. We also derive differential equations of collisionless motion of particles in the gravitational and magnetic fields. A special approximation of these equations is solved exactly, and its solution suggests that the superposition of the gravitational and magnetic fields acting on diamagnetic ice particles can account for the stability of Saturn's rings in its equatorial plane.