1. Space Telescope Symposium May 2005 Planetary Dynamics: Chaos & Cleanup 1 Space Telescope Symposium May 2005 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

2. Space Telescope Symposium May 2005 Planetary Dynamics: Chaos & Cleanup POrbital Period asemimajor axis nMean motion Mean longitude (=nt) Longitude of periapse Mass ratio m p /m * r H Hill radius = (/3) 1/3 a 1 Space Telescope Symposium May 2005

3. Planetary Dynamics: Chaos & Cleanup 1.Secular resonance: p-q’= const. 2. Kozai resonance: d/dt = 0 3. Close Encounters (r ~ Hill radius) 4. Two body mean motion resonances: pq’=const. 5. Three body mm resonances: pq’-r’’=const. 1 Space Telescope Symposium May 2005

4. Secular Instability Time Scales 1. Secular: T sec ~ P/ 2. Kozai: T koz ~ P (m 0 /m 2 )(a 2 /a) 3 where m 2 and a 2 are the mass and semimajor axis of the binary companion 3

5. Space Telescope Symposium May 2005 A Secular Resonance 4

6. Space Telescope Symposium May 2005 Consequences of the Kozai Instability 1. Large eccentricity, some of the time 2. Massive planets at small a 5

7. Space Telescope Symposium May 2005 HD 80606: Kozai? 6 Wu & Murray ApJ, 589, 605 (2003)

8. Space Telescope Symposium May 2005 Short Period Massive Planets 7 Wu & Murray ApJ, 589, 605 (2003)

9. Space Telescope Symposium May 2005 Crossing and Mean Motion Time Scales 1. Orbit crossing: T ej ~ P/(4 5/3 ) ~ 3x10 5 (P/12) (M J /M) 5/3 yrs 2. Mean Motion: T mm ~ P/(16e 2q ) e is initial free eccentricity, q=1,2,… For q>1, T mm >T ej 8

10. Space Telescope Symposium May 2005 Mean Motion Resonances 9

11. Space Telescope Symposium May 2005 Three Body Mean Motion Time Scales T tb ~ P/(    e 2q ) e is a representative initial free eccentricity, q=1,2,… For the outer solar system T tb ~ 10 8 yrs 10

12. Space Telescope Symposium May 2005 Three-body Resonances Holman & Wisdom AJ, 105, 1987 (1993)

13. Space Telescope Symposium May 2005 Consequences of Instability 1.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. Space Telescope Symposium May 2005 Consequences of Instability? 13