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Planetary Dynamics: Chaos & Cleanup

Planetary Dynamics: Chaos & Cleanup. From observations of our own and other systems we know: Secular resonances occur Mean motion resonances occur Chaotic motion occurs Collisions occur We suspect Ejections occur. 1. Space Telescope Symposium May 2005.

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Planetary Dynamics: Chaos & Cleanup

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  1. Planetary Dynamics: Chaos & Cleanup From observations of our own and other systems we know: Secular resonances occur Mean motion resonances occur Chaotic motion occurs Collisions occur We suspect Ejections occur 1 Space Telescope Symposium May 2005

  2. Planetary Dynamics: Chaos & Cleanup P Orbital Period a semimajor axis n Mean motion l Mean longitude (=nt) w Longitude of periapse m Mass ratio mp/m* rH Hill radius = (m/3)1/3a 1 Space Telescope Symposium May 2005

  3. Planetary Dynamics: Chaos & Cleanup • Secular resonance: pw-qw’= const. • 2. Kozai resonance: dw/dt = 0 • 3. Close Encounters (Dr ~ Hill radius) • 4. Two body mean motion resonances: • pl-ql’=const. • 5. Three body mm resonances: pl-ql’-rl’’=const. 1 Space Telescope Symposium May 2005

  4. Secular Instability Time Scales • Secular: Tsec ~ P/m • 2. Kozai: Tkoz ~ P (m0/m2)(a2/a)3 • where m2 and a2 are the mass and • semimajor axis of the binary companion 3

  5. A Secular Resonance 4

  6. Consequences of the Kozai Instability • Large eccentricity, some of the • time • 2. Massive planets at small a 5

  7. HD 80606: Kozai? 6 Wu & Murray ApJ, 589, 605 (2003)

  8. Short Period Massive Planets 7 Wu & Murray ApJ, 589, 605 (2003)

  9. Crossing and Mean Motion Time Scales 1. Orbit crossing: Tej ~ P/(4 m5/3) ~ 3x105 (P/12) (MJ/M)5/3 yrs 2. Mean Motion: Tmm ~ P/(16pme2q) e is initial free eccentricity, q=1,2,… For q>1, Tmm>Tej 8

  10. Mean Motion Resonances 9

  11. Three Body Mean Motion Time Scales Ttb ~ P/(16pm1m2e2q) e is a representative initial free eccentricity, q=1,2,… For the outer solar system Ttb~ 108 yrs 10

  12. Three-body Resonances Holman & Wisdom AJ, 105, 1987 (1993)

  13. Consequences of Instability • Ejection/accretion, usually of lighter body • 2. Remnant has substantial eccentricity • 3. Larger separation between survivors, • so the system tends to be more stable. • Note however that there are other ways • to produce dynamically stable spacings • and substantial eccentricities 12

  14. Consequences of Instability? 13

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