# American Institute of Mathematical Sciences

June  2017, 10(2): 467-479. doi: 10.3934/krm.2017018

## Approximate explicit stationary solutions to a Vlasov equation for planetary rings

 Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6,95125 Catania, Italy

Received  January 2015 Revised  May 2016 Published  November 2016

In this paper we consider a Vlasov or collisionless Boltzmann equation describing the dynamics of planetary rings. We propose a simple physical model, where the particles of the rings move under the gravitational Newtonian potential of two primary bodies. We neglect the gravitational forces between the particles. We use a perturbative technique, which allows to find explicit solutions at the first order and approximate solutions at the second order, by solving a set of two linear ordinary differential equations.

Citation: Armando Majorana. Approximate explicit stationary solutions to a Vlasov equation for planetary rings. Kinetic & Related Models, 2017, 10 (2) : 467-479. doi: 10.3934/krm.2017018
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##### References:
The density of mass of $\Psi_{1}$
The density of mass of $\Psi_{2}$
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