
Dynamics of Planetary Systems
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Content
- Cover
- Contents
- Preface
- 1. The two-body problem
- 1.1 Introduction
- 1.2 The shape of the Kepler orbit
- 1.3 Motion in the Kepler orbit
- 1.3.1 Orbit averages
- 1.3.2 Motion in three dimensions
- 1.3.3 Gauss's f and g functions
- 1.4 Canonical orbital elements
- 1.5 Units and reference frames
- 1.5.1 Time
- 1.5.2 Units for the solar system
- 1.5.3 The solar system reference frame
- 1.6 Orbital elements for exoplanets
- 1.6.1 Radial-velocity planets
- 1.6.2 Transiting planets
- 1.6.3 Astrometric planets
- 1.6.4 Imaged planets
- 1.7 Multipole expansion of a potential
- 1.7.1 The gravitational potential of rotating fluid bodies
- 1.8 Nearly circular orbits
- 1.8.1 Expansions for small eccentricity
- 1.8.2 The epicycle approximation
- 1.8.3 Orbits and the multipole expansion
- 1.9 Response of an orbit to an external force
- 1.9.1 Lagrange's equations
- 1.9.2 Gauss's equations
- 2. Numerical orbit integration
- 2.1 Introduction
- 2.1.1 Order of an integrator
- 2.1.2 The Euler method
- 2.1.3 The modified Euler method
- 2.1.4 Leapfrog
- 2.2 Geometric integration methods
- 2.2.1 Reversible integrators
- 2.2.2 Symplectic integrators
- 2.2.3 Variable timestep
- 2.3 Runge-Kutta and collocation integrators
- 2.3.1 Runge-Kutta methods
- 2.3.2 Collocation methods
- 2.4 Multistep integrators
- 2.4.1 Multistep methods for first-order differential equations
- 2.4.2 Multistep methods for Newtonian differential equations
- 2.4.3 Geometric multistep methods
- 2.5 Operator splitting
- 2.5.1 Operator splitting for Hamiltonian systems
- 2.5.2 Composition methods
- 2.5.3 Wisdom-Holman integrators
- 2.6 Regularization
- 2.6.1 Time regularization
- 2.6.2 Kustaanheimo-Stiefel regularization
- 2.7 Roundo error
- 2.7.1 Floating-point numbers
- 2.7.2 Floating-point arithmetic
- 2.7.3 Good and bad roundo behavior
- 3. The three-body problem
- 3.1 The circular restricted three-body problem
- 3.1.1 The Lagrange points
- 3.1.2 Stability of the Lagrange points
- 3.1.3 Surface of section
- 3.2 Co-orbital dynamics
- 3.2.1 Quasi-satellites
- 3.3 The hierarchical three-body problem
- 3.3.1 Lunar theory
- 3.4 Hill's problem
- 3.4.1 Periodic orbits in Hill's problem
- 3.4.2 Unbound orbits in Hill's problem
- 3.5 Stability of two-planet systems
- 3.6 Disk-driven migration
- 4. The N-body problem
- 4.1 Reference frames and coordinate systems
- 4.1.1 Barycentric coordinates
- 4.1.2 Astrocentric coordinates
- 4.1.3 Jacobi coordinates
- 4.2 Hamiltonian perturbation theory
- 4.2.1 First-order perturbation theory
- 4.2.2 The Poincaré-von Zeipel method
- 4.2.3 Lie operator perturbation theory
- 4.3 The disturbing function
- 4.4 Laplace coefficients
- 4.4.1 Recursion relations
- 4.4.2 Limiting cases
- 4.4.3 Derivatives
- 4.5 The stability of the solar system
- 4.5.1 Analytic results
- 4.5.2 Numerical results
- 4.6 The stability of planetary systems
- 5. Secular dynamics
- 5.1 Introduction
- 5.2 Lagrange-Laplace theory
- 5.3 The Milankovich equations
- 5.3.1 The Laplace surface
- 5.3.2 Stellar flybys
- 5.4 ZLK oscillations
- 5.4.1 Beyond the quadrupole approximation
- 5.4.2 High-eccentricity migration
- 6. Resonances
- 6.1 The pendulum
- 6.1.1 The torqued pendulum
- 6.1.2 Resonances in Hamiltonian systems
- 6.2 Resonance for circular orbits
- 6.2.1 The resonance-overlap criterion for nearly circular orbits
- 6.3 Resonance capture
- 6.3.1 Resonance capture in the pendulum Hamiltonian
- 6.3.2 Resonance capture for nearly circular orbits
- 6.4 The Neptune-Pluto resonance
- 6.5 Transit timing variations
- 6.6 Secular resonance
- 6.6.1 Resonance sweeping
- 7. Planetary spins
- 7.1 Precession of planetary spins
- 7.1.1 Precession and satellites
- 7.1.2 The chaotic obliquity of Mars
- 7.2 Spin-orbit resonance
- 7.2.1 The chaotic rotation of Hyperion
- 7.3 Andoyer variables
- 7.4 Colombo's top and Cassini states
- 7.5 Radiative forces on small bodies
- 7.5.1 Yarkovsky effect
- 7.5.2 YORP effect
- 8. Tides
- 8.1 The minimum-energy state
- 8.2 The equilibrium tide
- 8.2.1 Love numbers
- 8.3 Tidal friction
- 8.4 Spin and orbit evolution
- 8.4.1 Semimajor axis migration
- 8.4.2 Spinup and spindown
- 8.4.3 Eccentricity damping
- 8.5 Non-equilibrium tides
- 8.5.1 Planets on high-eccentricity orbits
- 8.5.2 Resonance locking
- 8.6 Tidal disruption
- 8.6.1 The Roche limit
- 8.6.2 Tidal disruption of regolith
- 8.6.3 Tidal disruption of rigid bodies
- 9. Planet-crossing orbits
- 9.1 Local structure of a planetesimal disk
- 9.2 Disk-planet interactions
- 9.2.1 Collisions
- 9.2.2 Gravitational stirring
- 9.3 Evolution of high-eccentricity orbits
- 9.4 The Galactic tidal field
- 9.5 The Oort cloud
- 9.6 The trans-Neptunian belt
- 9.7 Earth-crossing asteroids
- Appendix A. Physical, astronomical and solar-system constants
- Appendix B. Mathematical background
- B.1 Vectors
- B.2 Coordinate systems
- B.3 Vector calculus
- B.4 Fourier series
- B.5 Spherical trigonometry
- B.6 Euler angles
- B.7 Calculus of variations
- Appendix C. Special functions
- C.1 Kronecker delta and permutation symbol
- C.2 Delta function
- C.3 Gamma function
- C.4 Elliptic integrals
- C.5 Bessel functions
- C.6 Legendre functions
- C.7 Spherical harmonics
- C.8 Vector spherical harmonics
- Appendix D. Lagrangian and Hamiltonian dynamics
- D.1 Hamilton's equations
- D.2 Rotating reference frame
- D.3 Poisson brackets
- D.4 The propagator
- D.5 Symplectic maps
- D.6 Canonical transformations and coordinates
- D.7 Angle-action variables
- D.8 Integrable and non-integrable systems
- D.9 The averaging principle
- D.10 Adiabatic invariants
- D.11 Rigid bodies
- Appendix E. Hill and Delaunay variables
- E.1 Hill variables
- E.2 Delaunay variables
- Appendix F. The standard map
- F.1 Resonance overlap
- Appendix G. Hill stability
- Appendix H. The Yarkovsky effect
- Appendix I. Tidal response of rigid bodies
- I.1 Tidal disruption of a rigid body
- Appendix J. Relativistic effects
- J.1 The Einstein-Infeld-Hoffmann equations
- Problems
- References
- Index
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