Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Chapter 6

The Disturbing Function

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
   • Disturbing function : initialisation cells for the following notebook
   • Disturbing function : notebook
   1. Introduction
   2. The disturbing function
   3. Expansion using Legendre polynomials
   4. Literal expansion in orbital elements
   5. Literal expansion to second order
      • Section 6.5 : notebook
   6. Terms associated with a specific argument
   7. Use of the disturbing function
   8. Lagrange's planetary equations
   9. Classification of arguments in the disturbing function
      1. Secular terms
      2. Resonant terms
      3. Short period and small amplitude terms
   10. Sample calculations of the averaged disturbing function
       1. Terms associated with the 3:1 commensurability
          • Section 6.10.1 : notebook
       2. Terms associated with the 18:7 commensurability
          • Section 6.10.2 : notebook
   11. The effect of planetary oblateness
       • Orbital precession : animation
       • Section 6.11 : notebook
   12. Exercises
       • Answers (PDF)
7. Secular Perturbations
8. Resonant Perturbations
9. Chaos and Long-term Evolution
10. Planetary Rings

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

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