Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Chapter 3

The Restricted Three-Body Problem

1. Structure of the Solar System
2. The Two-Body Problem
3. THE RESTRICTED THREE-BODY PROBLEM
   1. Introduction
   2. Equations of motion
   3. The Jacobi integral
   4. The Tisserand relation
   5. Lagrangian equilibrium points
   6. Location of equilibrium points
      • Section 3.6 : notebook
      • Figure 3.7 : notebook
      • Figure 3.8 : notebook
      • Figure 3.10 : notebook
   7. Stability of equilibrium points
      • Section 3.7 : notebook
      • Figure 3.11 : notebook
      • Figure 3.12 : notebook
      • Figure 3.13 : notebook
      1. The collinear points
         • Stability : animation
      2. The triangular points
         • Stability : animation
   8. Motion near L₄ and L₅
      • Motion around L₄ : animation
      • Section 3.8 : notebook
   9. Tadpole and horseshoe orbits
      • Coorbital : animation
      • Figure 3.16 : notebook
      • Figure 3.17 : notebook
   10. Orbits and zero velocity curves
       • Figure 3.22 : notebook
   11. Trojan asteroids and satellites
       • Cruithne : animation
       • Figure 3.7 : notebook
   12. Janus and Epimetheus
       • Coorbital : animation
       • Figure 3.27 : notebook
   13. Hill's equations
       • Figure 3.28 : notebook
       • Figure 3.30 : notebook
   14. The effects of drag
       • Figure 3.32 : notebook
       1. Analysis of the Jacobi constant
       2. Linear stability of the L₄ and L₅ points
       3. Inertial drag forces
   15. Exercises
       • Answers (PDF)
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
10. Planetary Rings

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

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