Dynamical Chaos in Planetary Systems 3030521435, 9783030521431

Table of contents :
Preface
Contents
Part I Origins and Manifestations of Dynamical Chaos
1 Chaotic Behaviour
1.1 Pendulum, Resonances and Chaos
1.2 Models of Resonance
1.3 Interaction and Overlap of Resonances
1.4 Symplectic Maps in General
1.5 The Standard Map
1.6 The Separatrix Map
1.7 Generalized Separatrix Maps
1.8 Geometry of Chaotic Layers
2 Numerical Tools for Studies of Dynamical Chaos
2.1 Lyapunov Exponents
2.2 Fast Lyapunov Indicators
2.3 MEGNO Charts
2.4 Frequency Analysis
2.5 Sections of Phase Space
2.6 LCE Charts
2.7 Poincaré Recurrences
3 Lyapunov Timescales
3.1 Chirikov's Constant
3.2 Adiabatic Chaos
3.3 Lyapunov Exponents in Resonance Doublets and Triplets
3.4 Lyapunov Exponents in Resonance Multiplets
4 Diffusion Timescales
4.1 Diffusion Rates in Resonance Multiplets
4.2 Diffusion Rates in Resonance Doublets
4.3 Lyapunov and Diffusion Timescales: Relationships
4.4 Two Kinds of Hamiltonian Intermittency
5 Extents of Chaotic Domains
5.1 The Separatrix Split
5.2 Early Estimates of the Chaotic Layer Width
5.3 The Layer Width in Case of Non-adiabatic Chaos
5.4 The Layer Width in Case of Adiabatic Chaos
5.5 Marginal Resonances in Case of Non-adiabatic Chaos
5.6 Marginal Resonances in Case of Adiabatic Chaos
Part II Resonances and Chaos in the Solar System
6 Defying the Orrery Paradigm: Historical Background
7 Rotational Dynamics
7.1 Rotational Dynamics of Satellites
7.1.1 Hyperion and Other Chaotic Rotators
7.1.2 Spin-Orbit Resonances
7.1.3 Lyapunov Timescales of Chaotic Rotation
7.1.4 Widths of Chaotic Layers
7.1.5 Chaotic Planar Rotation and Chaotic Tumbling
7.1.6 Stability with Respect to Tilting the Axis of Rotation
7.2 Chaotic Obliquities of Planets
7.2.1 Relevant Spin-Orbit Resonances
8 Orbital Dynamics of Minor Bodies
8.1 Dynamics of Satellite Systems
8.1.1 The Miranda–Umbriel System
8.1.2 Generalization of the Separatrix Algorithmic Map
8.1.3 The Mimas–Tethys System
8.1.4 The Prometheus–Pandora System
8.2 Chaotic Dynamics of Asteroids and Kuiper Belt Objects
8.2.1 Resonant Structure of the Asteroid Belt
8.2.2 The Kuiper Belt Objects
8.2.3 Two-Body Resonances
8.2.4 Three-Body Resonances
8.2.5 Secular Resonances
8.3 Cometary Dynamics
8.3.1 Comets: Highly Chaotic
8.3.2 Lévy Flights at the Edge of Escape
8.4 Dynamical Environments of Small Bodies
8.4.1 Chaotic Zones Around Contact Binaries
8.4.2 Ida and Dactyl
8.4.3 Trans-Neptunian Objects, 2014 MU69 Among Them
9 Orbital Dynamics of Planets
9.1 Chaotic Giant Planets
Part III Dynamics of Exoplanets
10 Exoplanets: An Overview
10.1 History and Discoveries
10.2 Definition of a Planet
10.3 Typology and Properties of Exoplanets
10.3.1 Mass Function and Mass-Radius Relationship
10.3.2 Types of Exoplanets
10.3.3 Physical Types of Planetary Systems
10.4 Architecture and Dynamical Configurations
10.5 Resonant and Multi-Resonant Systems
11 Planetary Architecture: Stability, Packing and Ranging
11.1 Stability Criteria
11.1.1 Classical Results
11.1.2 Wisdom's Criterion: The μ2/7 Law
11.1.3 The Encounter Map
11.1.4 The Two-Dimensional Encounter Map
11.1.5 The Kepler Map Criterion: The μ2/5 Law
11.1.6 Hill's Criterion: The μ1/3 Law
11.1.7 The Holman–Wiegert Criteria
11.1.8 Lyapunov and Escape Times: Linear and Quadratic Relationships
11.2 Packing and Ranging Criteria
11.2.1 Historical Background: Kepler's Goblet
11.2.2 Dynamical Completeness
11.2.3 The Moriwaki–Nakagawa Criterion
12 Effects of Chaotic Clearing in Planetary Systems
12.1 Close-to-Coorbital Clearing
12.2 Circumbinary Clearing
12.3 Resonant Clearings
12.4 Inner Disintegration
13 Multiplanet Systems of Single Stars
13.1 Secular Planetary Dynamics
13.2 Location and Interaction of Resonances
13.2.1 The Outer Perturber Case
13.2.2 The Inner Perturber Case
13.3 Resonant and Formally Chaotic Exoplanet Systems
13.3.1 The Kepler-223 System
13.3.2 The Kepler-11 System
13.3.3 The GJ-876 System
13.3.4 The Kepler-36 System
13.3.5 The HD 12661 System
14 Planetary Systems of Multiple Stars
14.1 Circum-Companion Systems
14.1.1 The α Centauri System
14.1.2 The υ Andromedae System
14.1.3 The 55 Cancri System
14.1.4 The 16 Cygni System
14.2 Circumbinary Systems
14.2.1 Kepler's Circumbinary Planets
14.2.2 Migration and Chaos as System Architects
14.2.3 Chaotic Zones
14.2.4 Structure of Chaos Border
14.2.5 The Mass Parameter Threshold
15 The Lidov–Kozai Effect: Chaotic Implications
15.1 Multiplanet Systems
15.2 Planetary Systems of Binary Stars
15.3 Chaos Due to the Lidov–Kozai Effect
16 Epilogue
A Basic Notations
List of Abbreviations
B Astronomical Constants and Parameters
C The Melnikov–Arnold Integrals
Bibliography
Index