Physics of Planetary Rings : Celestial Mechanics of Continuous Media

Physics of Planetary Rings describes striking structures in the planetary rings of Saturn, Uranus, Jupiter and Neptune. In Saturn, the rings are stratified into thousands of ringlets united in a complex hierarchical structure with spiral waves and gaps; in Uranus, they are compressed into narrow str...

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Main Authors: Fridman, Alexei M., Gorkavyi, Nikolai N. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1999, 1999
Edition:1st ed. 1999
Series:Astronomy and Astrophysics Library
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 3. Derivation of the Basic Equations for the “Plane” Functions
  • 3.1 Order-of-Magnitude Estimates of the Terms in the Initial Equations
  • 3.2 The Two Limiting Cases of Astrophysical Discs
  • 3.3 Limitations of the Characteristic Times of Processes Studied in the Two-Dimensional Approximation
  • 3.4 Closed System of Integro-differential Equations for a Barotropic Disc
  • 4. Closed Set of Differential Equations for a Polytropic Disc in an External Gravitational Field
  • 4.1 Derivation of the Two-Dimensional Equations
  • 5. Closed Set of Differential Equations for a Polytropic Self-gravitating Disc
  • 5.1 Derivation of the Two-Dimensional Equations
  • 5.2 Why Does the Gradient of the Plane Pressure Not Have the Physical Meaning of a Force?
  • 6. Conclusion
  • 1. Derivation of a Closed Set of Integro-differential Equations
  • 2. Derivation of the Dispersion Equation Describing the Three-Dimensional Perturbations
  • 4. Dispersion Relation for Waves in the Plane of the Disc
  • 5. The Role of Perturbations Along the Rotation Axis
  • 5.1 Condition for Neglecting Mass Transfer Along the Rotation Axis
  • 5.1.1 General Case
  • 5.1.2 Isothermal Disc
  • 6. Conclusion
  • III. Derivation of the Linearised Equations for Oscillations of a Viscous Disc
  • 1. Derivation of the Linearised Equations for Oscillations of a Viscous Uniformly Rotating Disc
  • 2. Derivation of the Linearised Equations for Oscillations of a Viscous Differentially Rotating Disc of Inelastic Particles with Account of External Matter Fluxes
  • 3. Derivation of the General Dispersion Equation
  • IV. Evaluating the Gravitational Potential Inside and Outside a Triaxial Ellipsoid
  • 1. Potential Inside the Ellipsoid
  • 2. Potential Outside the Ellipsoid
  • V. A Drift Mechanism for the Formation of the Cassini Division
  • 1. Introduction
  • 2. Statement of the Problem
  • 3. Derivation of the Non-linear Momentum Conservation Equations
  • 4. Time-Averaged Non-linear Momentum Conservation Equations
  • 1. Introduction
  • 2. Observational Data
  • 3. Celestial Mechanics Minimum
  • 4. Elementary Particle Dynamics. I Rigid Body Collisions
  • 5. Elementary Particle Dynamics. II Ring Cosmogony
  • 6. Elementary Particle Dynamics. III Wave, Photometric, and Other Effects
  • 7. Collective Dynamics of Disc Particles. I Formalism
  • 8. Collective Dynamics of Disc Particles. II Stability Analysis
  • 9. Resonance Effects in Planetary Rings. I Spiral Waves
  • 10. Resonance Effects in Planetary Rings. II Narrow Ringlets and Satellites
  • 11. Formation and Stability of the Uranian Rings
  • 12. Origin, Dynamics, and Stability of the Neptunian Rings
  • 13. Self-organisation of the Solar System
  • 14. Space Studies of the Outer Planets
  • Conclusion
  • Appendices I. The Possibility of Studying the Dynamics of Astrophysical Discs in a Two-Dimensional Approach
  • 1. Introduction
  • 2. Original Equations for the “Volume” Functions
  • 2.1 Initial Dynamic Equations
  • 2.2 Equation of State
  • Gaps or Wavetrains?
  • 9. Estimate of the Maximum Width of a Gap Produced by a Density Wave
  • 10. Some Additional Remarks
  • VI. Resonance Structures in Saturn’s C Ring
  • References