Credit: NASA/JPL/Space Science Institute
Chapter One
1. Structure of the Solar System
1.1 Introduction
1.2 The belief in number
1.3 Kepler's laws of planetary motion
1.4 Newton's universal law of gravitation
1.5 The Titius-Bode 'law'
1.6 Resonance in the Solar System
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1.6.1 The planetary system
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1.6.2 The Jupiter system
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1.6.3 The Saturn system
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1.6.4 The Uranus system
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1.6.5 The Neptune system
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1.6.6 The Pluto system
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1.6.7 The asteroid belt
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1.6.8 Comets, meteors and dust
1.7 The preference for commensurability
1.8 Recent developments
1.9 Exercises
Chapter Two
2. The Two-Body Problem
2.1 Introduction
2.2 Equations of motion
2.3 Orbital position and velocity
2.4 The mean and eccentric anomalies
2.5 Elliptical expansions
2.6 The guiding centre apporximation
2.7 Barycentric orbits
2.8 The orbit in space
2.9 Perturbed orbits
2.10 Hamiltonian formulation
2.11 Exercises
Chapter Three
3. The Restricted Three-Body Problem
3.1 Introduction
3.2 Equations of motion
3.3 The Jacobi integral
3.4 The Tisserand relation
3.5 Lagrangian equilibrium points
3.6 Location of equilibrium points
3.7 Stability of equilibrium points
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3.7.1 The collinear points
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3.7.2 The triangular points
3.8 Motion near L4 and L5
3.9 Tadpole and horseshoe orbits
3.10 Orbits and zero velocity curves
3.11 Trojan asteroids and satellites
3.12 Janus and Epimetheus
3.13 Hill's equations
3.14 The effects of drag
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3.14.1 Analysis of the Jacobi constant
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3.14.2 Linear stability of the L4 and L5 points
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3.14.3 Inertial drag forces
3.15 Exercises
Chapter Four
4. Tides, Rotation and Shape
4.1 Introduction
4.2 The tidal bulge
4.3 Potential theory
4.4 Tidal deformation
4.5 Rotational deformation
4.6 The Darwin-Radau relation
4.7 Shapes and internal structures of satellites
4.8 The Roche zone
4.9 Tidal torques
4.10 Satellite tides
4.11 Tidal heating of Io
4.12 Tides on Titan
4.13 Tidal evolution
4.14 The double synchronous state
4.15 Exercises
Chapter Six
6. The Disturbing Function
6.1 Introduction
6.2 The disturbing function
6.3 Expansion using Legendre polynomials
6.4 Literal expansion in orbital elements
6.5 Literal expansion to second order
6.6 Terms associated with a specific argument
6.7 Use of the disturbing function
6.8 Lagrange's planetary equations
6.9 Classification of arguments in the disturbing function
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6.9.1 Secular terms
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6.9.2 Resonant terms
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6.9.3 Short period and small amplitude terms
6.10 Sample calculations of the averaged disturbing function
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6.10.1 Terms associated with the 3:1 commensurability
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6.10.2 Terms associated with the 18:7 commensurability
6.11 The effect of planetary oblateness
6.12 Exercises
Chapter Seven
7. Secular Perturbations
7.1 Introduction
7.2 Secular perturbations for two planets
7.3 Jupiter and Saturn
7.4 Free and forced elements
7.5 Jupiter, Saturn and a test particle
7.6 Gauss's averaging method
7.7 Generalised secular perturbations
7.8 Secular theory for the solar system
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Secular evolution of the orbits of the inner planets: animation
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Secular evolution of the orbits of the outer planets: animation
7.9 Generalised free and forced elements
7.10 Hirayama families and the IRAS dust bands
7.11 Secular resonances
7.12 Higher order secular theory
7.13 Exercises
Chapter Eight
8. Resonant Perturbations
8.1 Introduction
8.2 The geometry of resonance
8.3 The physics of resonance
8.4 Variation of orbital elements
8.5 Resonance in the circular restricted three-body problem
8.6 The pendulum model
8.7 Libration width
8.8 The Hamiltonian approach
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8.8.1 The e and e' resonances
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8.8.2 The e^2, e'^2, I^2 and I'^2 resonances
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8.8.3 The e^3 and e'^3 resonances
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8.8.4 The ee' and II' resonances
8.9 The 2:1 resonance
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8.9.1 Exact resonance
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8.9.2 Medium amplitude libration
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8.9.3 Large amplitude libration
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8.9.4 Apocentric libration
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8.9.5 Internal circulation
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8.9.6 External circulation
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8.9.7 Other types of motion
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8.9.8 Comparison with analytical theory
8.10 The 3:1 and 7:4 resonances
8.11 Additional resonances and resonance splitting
8.12 Resonant encounters
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8.12.1 Encounters with first-order resonances
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8.12.2 Encounters with second-order resonances
8.13 The dynamics of capture and evolution in resonance
8.14 Two-body resonances in the solar system
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8.14.1 The Titan-Hyperion resonance
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8.14.2 The Mimas-Tethys resonance
8.15 Resonant encounters in satellite systems
8.16 Three-body resonance
8.17 The Laplace resonance
8.18 Secular and resonant motion
8.19 LONGSTOP Uranus
8.20 Pulsar planets
8.21 Exercises
Chapter Nine
9. Chaos and Long-Term Evolution
9.1 Introduction
9.2 The geometry of resonance
9.3 Regular and chaotic orbits
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9.3.1 The Poincaré surface of section
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9.3.2 Regular orbits
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9.3.3 Chaotic orbits
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9.3.4 The Lyapounov characteristic exponent
9.4 Chaos in the circular restricted problem
9.5 Algebraic mappings
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9.5.1 The standard map
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9.5.2 Resonance maps
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9.5.3 Encounter maps
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9.5.4 N-body maps
9.6 Separatrices and resonance overlap
9.7 The rotation of Hyperion
9.8 The Kirkwood gaps
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9.8.1 Resonant structure of the asteroid belt
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9.8.2 The 3:1 resonance
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9.8.3 Other resonances
9.9 The Neptune-Pluto system
9.10 The stability of the Solar System
9.11 Exercises
Chapter Ten
10. Planetary Rings
10.1 Introduction
10.2 Planetary ring systems
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10.2.1 The rings of Jupiter
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10.2.2 The rings of Saturn
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10.2.3 The rings of Uranus
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10.2.4 The rings of Neptune
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10.2.5 Rings and satellites
10.3 Resonances in the rings
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10.3.1 Perturbations in semi-major axis and corotation resonances
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10.3.2 Perturbations in eccentricity and Lindblad resonances
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10.3.3 Perturbations in inclination and vertical resonances
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10.3.4 Locations of resonances
10.4 Density waves and bending waves
10.5 Narrow rings and sharp edges
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10.5.1 Spreading timescales
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10.5.2 Localised effects of satellite perturbations
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10.5.3 Shepherding satellites and radial confinement
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10.5.4 Eccentric and inclined rings
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10.5.5 Embedded satellites and horseshoe orbits
10.6 The Encke gap and Pan
10.7 The F ring of Saturn
10.8 The Adams ring of Neptune
10.9 The evolution of rings
10.10 The Earth's dust ring
10.11 Exercises