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- Title
Modeling of the Origin of Saturn's Dense (Visible) Rings Taking into Account Gravitational and Magnetic Fields. The Tchernyi‒Kapranov Effect.
- Authors
Tchernyi, V. V.; Kapranov, S. V.
- Abstract
A mathematical model is proposed for the origin of Saturn's dense (visible) rings, which has been a mystery for 400 years since Galileo saw them in 1610. Despite the technological perfection of the Cassini probe, which explored the Saturn system in 2004‒2017, the mission did not receive a final answer to this question. The available gravitational models cannot explain the origin of the stable disk of rings at the equator of the planet, but they can answer the question of where the ice in the rings came from. Therefore, we have added the action of the Saturn's magnetic field to consideration. We study the motion of ice particles within the Roche limit that could have formed as a result of the collision of two moons or the destruction of a Titan-sized body or Saturn's satellite. The problem of motion of a diamagnetic particle in the Saturn's gravitational and magnetic fields is solved. It is shown that, as a result of motion, diamagnetic ice particles form a disk system of rings on the magnetic equator of the planet. The effect of the Saturn's magnetic field (the Tchernyi‒Kapranov effect) is manifested in the magnetic anisotropic accretion of diamagnetic ice particles, which form a disk of rings, and the subsequent stabilization of the entire system of dense rings occurs. The solution of the problem begins with the determination of the magnetization and potential energy of a spherical diamagnetic particle in a magnetic field. We have derived an equation that relates the permeability of a diamagnet to its magnetization, which is an analogue of the Clausius‒Mossotti relation for a dielectric. It is used to study the dynamics of motion of a diamagnetic particle in the Saturn's gravitational and magnetic fields. Next, we solve the problem of a single magnetized sphere and a spherical particle among identical diamagnetic particles scattered in a disk-shaped structure. Differential equations of collisionless motion of diamagnetic particles in the Saturn's gravitational and magnetic fields are derived. A special, physically justified approximation of these equations is analytically solved. It suggests that the superposition of the gravitational and magnetic fields acting on a diamagnetic ice particle can explain the stability of Saturn's dense rings in the Saturn's equatorial plane. Due to this fact, the role of magnetism in stabilizing rings of other planets turns out to be universal.
- Subjects
GALILEI, Galileo, 1564-1642; CASSINI (Spacecraft); GRAVITATIONAL fields; MAGNETIC fields; ICING (Meteorology); MAGNETIC particles; EQUATIONS of motion; SATURN (Planet); PROTOPLANETARY disks; TITAN (Satellite); COLLISIONLESS plasmas
- Publication
Optics & Spectroscopy, 2023, Vol 131, Issue 5, p327
- ISSN
0030-400X
- Publication type
Article
- DOI
10.1134/S0030400X24700085