**Structure of the Solar System**- Introduction
- The belief in number
- Kepler's laws of planetary motion
- Newton's universal law of gravitation
- The Titius-Bode 'law'
- Resonance in the solar system
- The planetary system
- The Jupiter system
- The Saturn system
- The Uranus system
- The Neptune system
- The Pluto system
- The asteroid belt
- Comets, meteors and dust

- The preference for commensurability
- Recent developments
- Exercises

**The Two-Body Problem**- Introduction
- Equations of motion
- Orbital position and velocity
- The mean and eccentric anomalies
- Elliptic expansions
- The guiding centre approximation
- Barycentric orbits
- The orbit in space
- Perturbed orbits
- Hamiltonian formulation
- Exercises

**The Restricted Three-Body Problem**- Introduction
- Equations of motion
- The Jacobi integral
- The Tisserand relation
- Lagrangian equilibrium points
- Location of equilibrium points
- Stability of equilibrium points
- The collinear points
- The triangular points

- Motion near
*L*_{4}and*L*_{5} - Tadpole and horseshoe orbits
- Orbits and zero velocity curves
- Trojan asteroids and satellites
- Janus and Epimetheus
- Hill's equations
- The effects of drag
- Analysis of the Jacobi constant
- Linear stability of the
*L*_{4}and*L*_{5}points - Inertial drag forces

- Exercises

**Tides, Rotation and Shape**- Introduction
- The tidal bulge
- Potential theory
- Tidal deformation
- Rotational deformation
- The Darwin-Radau relation
- Shapes and internal structures of satellites
- The Roche zone
- Tidal torques
- Satellite tides
- Tidal heating of Io
- Tides on Titan
- Tidal evolution
- The double synchronous state
- Exercises

**Spin-Orbit Coupling**- Introduction
- Tidal despinning
- The permanent quadrupole moment
- Spin-orbit resonance
- Capture into resonance
- Forced librations
- Surface of section
- Exercises

**The Disturbing Function**- Introduction
- The disturbing function
- Expansion using Legendre polynomials
- Literal expansion in orbital elements
- Literal expansion to second order
- Terms associated with a specific argument
- Use of the disturbing function
- Lagrange's planetary equations
- Classification of arguments in the disturbing function
- Secular terms
- Resonant terms
- Short period and small amplitude terms

- Sample calculations of the averaged disturbing function
- Terms associated with the 3:1 commensurability
- Terms associated with the 18:7 commensurability

- The effect of planetary oblateness
- Exercises

**Secular Perturbations**- Introduction
- Secular perturbations for two planets
- Jupiter and Saturn
- Free and forced elements
- Jupiter, Saturn and a test particle
- Gauss's averaging method
- Generalised secular perturbations
- Secular theory for the solar system
- Generalised free and forced elements
- Hirayama families and the
*IRAS*dust bands - Secular resonance
- Higher order secular theory
- Exercises

**Resonant Perturbations**- Introduction
- The geometry of resonance
- The physics of resonance
- Variation of orbital elements
- Resonance in the circular restricted three-body problem
- The pendulum model
- Libration width
- The Hamiltonian approach
- The
*e*and*e'*resonances - The
*e*^{2},*e'*^{2},*I*^{2}and*I'*^{2}resonances - The
*e*^{3}and*e'*^{3}resonances - The
*ee'*and*II'*resonances

- The
- The 2:1 resonance
- Exact resonance
- Medium amplitude libration
- Large amplitude libration
- Apocentric libration
- Internal circulation
- External circulation
- Other types of motion
- Comparison with analytical theory

- The 3:1 and 7:4 resonances
- Additional resonances and resonance splitting
- Resonant encounters
- Encounters with first-order resonances
- Encounters with second-order resonances

- The dynamics of capture and evolution in resonance
- Two-body resonances in the solar system
- The Titan-Hyperion resonance
- The Mimas-Tethys resonance

- Resonant encounters in satellite systems
- Three-body resonance
- The Laplace resonance
- Secular and resonant motion
*LONGSTOP*Uranus- Pulsar planets
- Exercises

**Chaos and Long-Term Evolution**- Introduction
- Sensitive dependence on initial conditions
- Regular and chaotic orbits
- The Poincaré surface of section
- Regular orbits
- Chaotic orbits
- The Lyapounov characteristic exponent

- Chaos in the circular restricted problem
- Algebraic mappings
- The standard map
- Resonance maps
- Encounter maps
*N*-body maps

- Separatrices and resonance overlap
- The rotation of Hyperion
- The Kirkwood gaps
- Resonant structure of the asteroid belt
- The 3:1 resonance
- Other resonances

- The Neptune-Pluto system
- The stability of the solar system
- Exercises

**Planetary Rings**- Introduction
- Planetary ring systems
- The rings of Jupiter
- The rings of Saturn
- The rings of Uranus
- The rings of Neptune
- Rings and satellites

- Resonances in the rings
- Perturbations in semi-major axis and corotation resonances
- Perturbations in eccentricity and Lindblad resonances
- Perturbations in inclination and vertical resonances
- Locations of resonances

- Density waves and bending waves
- Narrow rings and sharp edges
- Spreading timescales
- Localised effects of satellite perturbations
- Shepherding satellites and radial confinement
- Eccentric and inclined rings
- Embedded satellites and horseshoe orbits

- The Encke gap and Pan
- The F ring of Saturn
- The Adams ring of Neptune
- The evolution of rings
- The Earth's dust ring
- Exercises

**Appendix - Solar System Data**- Introduction
- Astronomical constants
- Julian date
- Orbital elements of the planets and their variation
- Planets, satellites and rings
- Asteroids, Centaurs, trans-Neptunian objects and comets

**Appendix - Expansion of the Disturbing Function**- Introduction

**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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