Panoramic Rings

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

  • 1.6.1 The planetary system

  • 1.6.2 The Jupiter system

  • 1.6.3 The Saturn system

  • 1.6.4 The Uranus system

  • 1.6.5 The Neptune system

  • 1.6.6 The Pluto system

  • 1.6.7 The asteroid belt

  • 1.6.8 Comets, meteors and dust

1.7 The preference for commensurability

1.8 Recent developments

1.9 Exercises

 
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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

 
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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

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​

  • Figure 3.32: notebook

  • 3.14.1 Analysis of the Jacobi constant

  • 3.14.2 Linear stability of the L4 and L5 points

  • 3.14.3 Inertial drag forces

3.15 Exercises

 
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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

 
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Chapter Five

5. Spin-Orbit Coupling

5.1 Introduction

5.2 Tidal despinning

5.3 ​The permanent quadrupole moment

5.4 Spin-orbit resonance

5.5 Capture into resonance

5.6 Forced librations

5.7 Surface of section

5.8 Exercises

 
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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

  • 6.9.1 Secular terms

  • 6.9.2 Resonant terms

  • 6.9.3 Short period and small amplitude terms

6.10 Sample calculations of the averaged disturbing function

6.11 The effect of planetary oblateness

6.12 Exercises

 
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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

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

 
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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

8.9 The 2:1 resonance​

  • 8.9.1 Exact resonance

  • 8.9.2 Medium amplitude libration

  • 8.9.3 Large amplitude libration

  • 8.9.4 Apocentric libration

  • 8.9.5 Internal circulation

  • 8.9.6 External circulation

  • 8.9.7 Other types of motion

  • 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

8.13 The dynamics of capture and evolution in resonance​

8.14 Two-body resonances in the solar system

  • 8.14.1 The Titan-Hyperion resonance

  • 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

 
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Chapter Nine

9. Chaos and Long-Term Evolution

9.1 Introduction

9.2 The geometry of resonance

​9.3 ​Regular and chaotic orbits

  • 9.3.1 The Poincaré surface of section​

  • 9.3.2 Regular orbits

  • 9.3.3 Chaotic orbits

  • 9.3.4 The Lyapounov characteristic exponent

9.4 Chaos in the circular restricted problem

9.5 Algebraic mappings

  • ​9.5.1 The standard map

  • 9.5.2 Resonance maps

  • 9.5.3 Encounter maps

  • 9.5.4 N-body maps

9.6 Separatrices and resonance overlap

9.7 The rotation of Hyperion

​9.8 The Kirkwood gaps

  • 9.8.1 Resonant structure of the asteroid belt

  • 9.8.2 The 3:1 resonance

  • 9.8.3 Other resonances​

9.9 The Neptune-Pluto system​

9.10 The stability of the Solar System

9.11 Exercises

 
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Chapter Ten

10. Planetary Rings

10.1 Introduction

10.2 Planetary ring systems

  • Figure 10.1: notebook

  • 10.2.1 The rings of Jupiter

  • 10.2.2 The rings of Saturn

  • 10.2.3 The rings of Uranus

  • 10.2.4 The rings of Neptune

  • 10.2.5 Rings and satellites

​10.3 ​Resonances in the rings

10.4 Density waves and bending waves

10.5 Narrow rings and sharp edges

  • ​10.5.1 Spreading timescales

  • 10.5.2 Localised effects of satellite perturbations

  • 10.5.3 Shepherding satellites and radial confinement

  • 10.5.4 Eccentric and inclined rings

  • 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