Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Table of Contents

1. Structure of the Solar System
   1. Introduction
   2. The belief in number
   3. Kepler's laws of planetary motion
   4. Newton's universal law of gravitation
   5. The Titius-Bode 'law'
   6. Resonance in the solar system
      1. The planetary system
      2. The Jupiter system
      3. The Saturn system
      4. The Uranus system
      5. The Neptune system
      6. The Pluto system
      7. The asteroid belt
      8. Comets, meteors and dust
   7. The preference for commensurability
   8. Recent developments
   9. Exercises

2. The Two-Body Problem
   1. Introduction
   2. Equations of motion
   3. Orbital position and velocity
   4. The mean and eccentric anomalies
   5. Elliptic expansions
   6. The guiding centre approximation
   7. Barycentric orbits
   8. The orbit in space
   9. Perturbed orbits
   10. Hamiltonian formulation
   11. Exercises

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
   7. Stability of equilibrium points
      1. The collinear points
      2. The triangular points
   8. Motion near L₄ and L₅
   9. Tadpole and horseshoe orbits
   10. Orbits and zero velocity curves
   11. Trojan asteroids and satellites
   12. Janus and Epimetheus
   13. Hill's equations
   14. The effects of drag
       1. Analysis of the Jacobi constant
       2. Linear stability of the L₄ and L₅ points
       3. Inertial drag forces
   15. Exercises

4. Tides, Rotation and Shape
   1. Introduction
   2. The tidal bulge
   3. Potential theory
   4. Tidal deformation
   5. Rotational deformation
   6. The Darwin-Radau relation
   7. Shapes and internal structures of satellites
   8. The Roche zone
   9. Tidal torques
   10. Satellite tides
   11. Tidal heating of Io
   12. Tides on Titan
   13. Tidal evolution
   14. The double synchronous state
   15. Exercises

5. Spin-Orbit Coupling
   1. Introduction
   2. Tidal despinning
   3. The permanent quadrupole moment
   4. Spin-orbit resonance
   5. Capture into resonance
   6. Forced librations
   7. Surface of section
   8. Exercises

6. The Disturbing Function
   1. Introduction
   2. The disturbing function
   3. Expansion using Legendre polynomials
   4. Literal expansion in orbital elements
   5. Literal expansion to second order
   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
       2. Terms associated with the 18:7 commensurability
   11. The effect of planetary oblateness
   12. Exercises

7. Secular Perturbations
   1. Introduction
   2. Secular perturbations for two planets
   3. Jupiter and Saturn
   4. Free and forced elements
   5. Jupiter, Saturn and a test particle
   6. Gauss's averaging method
   7. Generalised secular perturbations
   8. Secular theory for the solar system
   9. Generalised free and forced elements
   10. Hirayama families and the IRAS dust bands
   11. Secular resonance
   12. Higher order secular theory
   13. Exercises

8. Resonant Perturbations
   1. Introduction
   2. The geometry of resonance
   3. The physics of resonance
   4. Variation of orbital elements
   5. Resonance in the circular restricted three-body problem
   6. The pendulum model
   7. Libration width
   8. The Hamiltonian approach
      1. The e and e' resonances
      2. The e², e'², I² and I'² resonances
      3. The e³ and e'³ resonances
      4. The ee' and II' resonances
   9. The 2:1 resonance
      1. Exact resonance
      2. Medium amplitude libration
      3. Large amplitude libration
      4. Apocentric libration
      5. Internal circulation
      6. External circulation
      7. Other types of motion
      8. Comparison with analytical theory
   10. The 3:1 and 7:4 resonances
   11. Additional resonances and resonance splitting
   12. Resonant encounters
       1. Encounters with first-order resonances
       2. Encounters with second-order resonances
   13. The dynamics of capture and evolution in resonance
   14. Two-body resonances in the solar system
       1. The Titan-Hyperion resonance
       2. The Mimas-Tethys resonance
   15. Resonant encounters in satellite systems
   16. Three-body resonance
   17. The Laplace resonance
   18. Secular and resonant motion
   19. LONGSTOP Uranus
   20. Pulsar planets
   21. Exercises

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
   5. Algebraic mappings
      1. The standard map
      2. Resonance maps
      3. Encounter maps
      4. N-body maps
   6. Separatrices and resonance overlap
   7. The rotation of Hyperion
   8. The Kirkwood gaps
      1. Resonant structure of the asteroid belt
      2. The 3:1 resonance
      3. Other resonances
   9. The Neptune-Pluto system
   10. The stability of the solar system
   11. Exercises

10. Planetary Rings
    1. Introduction
    2. Planetary ring systems
       1. The rings of Jupiter
       2. The rings of Saturn
       3. The rings of Uranus
       4. The rings of Neptune
       5. Rings and satellites
    3. Resonances in the rings
       1. Perturbations in semi-major axis and corotation resonances
       2. Perturbations in eccentricity and Lindblad resonances
       3. Perturbations in inclination and vertical resonances
       4. Locations of resonances
    4. Density waves and bending waves
    5. Narrow rings and sharp edges
       1. Spreading timescales
       2. Localised effects of satellite perturbations
       3. Shepherding satellites and radial confinement
       4. Eccentric and inclined rings
       5. Embedded satellites and horseshoe orbits
    6. The Encke gap and Pan
    7. The F ring of Saturn
    8. The Adams ring of Neptune
    9. The evolution of rings
    10. The Earth's dust ring
    11. Exercises

1. Appendix - Solar System Data
   1. Introduction
   2. Astronomical constants
   3. Julian date
   4. Orbital elements of the planets and their variation
   5. Planets, satellites and rings
   6. Asteroids, Centaurs, trans-Neptunian objects and comets

2. Appendix - Expansion of the Disturbing Function
   1. Introduction

3. References

• the latest list of known errors,
• answers to the exercise questions,
• a compilation of the symbols used in the book, and
• the references cited in Solar System Dynamics.

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