Collective Dynamics of Disc Particles I Formalism
One can understand the reasons why the brightness of the Saturnian A ring shows an azimuthal asymmetry by considering the dynamics of the separate particles. However, the layering of the Saturnian rings and the occurrence of other spatial structures in the planetary rings are caused by collective processes and it is natural to study those in the framework of a hydrodynamic model where the “gas” of the colliding macroparticles is described in the same way as an ordinary molecular gas. The results of Chaps. 4 and 5 show that one can take as a typical ring particle a practically completely inelastic loose meter-size sphere. One must here take into account the gravitational field of such particles; this plays an important role in collision processes and in the break-up of large bodies and the motion of the small fragments. It is impossible to speak about the applicability of hydrodynamics to planetary rings without indicating the characteristic sizes and time scales of the processes which are described; they must be significantly larger than the mean free path and the mean free flight time of a particle, respectively. We shall show in Chap. 8 that these inequalities are satisfied for the large-scale processes in which we are interested.
KeywordsKinetic Equation Moment Equation Transport Theory Thermal Conductivity Coefficient Collective Dynamics
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