Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Chapter 9

Chaos and Long-Term Evolution

1. Structure of the Solar System
2. The Two-Body Problem
3. The Restricted Three-Body Problem
4. Tides, Rotation and Shape
5. Spin-Orbit Coupling
6. The Disturbing Function
7. Secular Perturbations
8. Resonant Perturbations
9. CHAOS AND LONG-TERM EVOLUTION
   1. Introduction
   2. Sensitive dependence on initial conditions
   3. Regular and chaotic orbits
      1. The Poincaré surface of section
      2. Regular orbits
      3. Chaotic orbits
      4. The Lyapounov characteristic exponent
   4. Chaos in the circular restricted problem
      • Interior surface of section : animation
      • Exterior surface of section : animation
   5. Algebraic mappings
      1. The standard map
      2. Resonance maps
      3. Encounter maps
      4. N-body maps
   6. Separatrices and resonance overlap
      • Figure 9.23 : notebook
   7. The rotation of Hyperion
   8. The Kirkwood gaps
      1. Resonant structure of the asteroid belt
         • Asteroids : animation
      2. The 3:1 resonance
      3. Other resonances
   9. The Neptune-Pluto system
      • Figures 9.33-34 : notebook
      • Figure 9.35 : notebook
   10. The stability of the solar system
   11. Exercises
       • Answers (PDF)
10. Planetary Rings

1. Appendix - Solar System Data
2. Appendix - Expansion of the Disturbing Function
3. References (PDF)

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