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Secular, Kozai , mean- motion resonances

D.N.C. Lin D epartment o f A stronomy & A strophysics University of California, Santa Cruz. Secular, Kozai , mean- motion resonances. Lecture 4, AY 222 Apr 11 th , 2012. A system of N planets. Normal modes. 7au. 9.7 au. Secular resonance.

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Secular, Kozai , mean- motion resonances

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  1. D.N.C. Lin Department of Astronomy & Astrophysics University of California, Santa Cruz Secular, Kozai, mean-motion resonances Lecture 4, AY 222 Apr 11th, 2012

  2. A system of N planets

  3. Normal modes 7au 9.7 au

  4. Secular resonance Additional contributor to precession : disk self gravity =0 It is possible for for a finite h, lock-step precession & Sweeping secular resonance => e can increase monotonically to large amplitudes. 18/24

  5. Kozai resonance in inclined systems When => 19/24

  6. High order terms and tidal contribution 20/24

  7. Mean motion resonances Two secular frequencies: periastron precession and conjunction drift. A Hamiltonian approach: dpi/dt=-dH/dqi dqi/dt=dH/dpi Energy (=a) as well as Angular momentum exchange 21/24

  8. Eccentricity excitation and transition to chaos Consider N equal M & Da planets with e excitation => nonlinear effect=> chaos 22/24

  9. Overlapping resonances & dynamical instability Dynamical filling factor & gas damping 23/24

  10. Many other competing forces Orbital changes may be due to: 1) Mass accretion and potential change Planet-disk interaction, Planet-magnetosphere interaction, Planet-star tidal interaction, Stellar radiation & wind, Planetesimal scattering, 7) Planetary mass loss, Perturbation by binary and field stars, Higher order contributions 24/24

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