lec25_30nov2011

lec25_30nov2011 - Recall: Resonant systems common,...

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Ge/Ay133 Planetary Dynamics
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Orbital elements (3-D), & time evolution:
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What ARE Lyapounov exponents and times? Suppose that two orbits are separated in phase space by d, and that d follows d = d 0 e - γ (t-t0) G is the Lyapounov exponent, and 1/ γ is the Lyapounov time. Numerically, G = lim ln(d/d 0 )/(t-t 0 ) As t → ∞. For regular orbits, γ → 0. Regular ↑ Chaotic ↓
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Libration Rotation Chaos in the outer S.S.: Uranus’s orbit can go from librating to rotating behavior. Chaotic, but
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The exact details are sensitive to the presence or absence of remnant gas or planetesimal disks: As disks dissipate, a stable system can become unstable…
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Unformatted text preview: Recall: Resonant systems common, & migrate more slowly in a disk From Armitage. Why? Couple of reasons, including wider gap opening and exchange of momentum between the interacting planets & disk. Simulation of two-planet interactions, with slow outer planet migration: HD 12661 Might this explain some of the unusual exo-planets? http://astron.berkeley.edu/~echiang/ Are HD 12661 and/or Ups And apsidally locked? http://astron.berkeley.edu/~echiang/ More recent analyses suggest e UpsAndc is variable! Need an impulsive scatterer. As disk disperses, lose planet?...
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lec25_30nov2011 - Recall: Resonant systems common,...

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