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“Spin-orbit resonances: our Solar System in context” Alexandre Correia (University of Aveiro / Paris Observatory) IAU Symposium 276, Turin, 14 th October 2010
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What is a spin-orbit resonance (SOR) ? : rotation angle ε: obliquity φ: precession angle
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: longitude of the node ω Ω What is a spin-orbit resonance (SOR) ? i: inclination M: mean anomaly : longitude of the periastron
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: longitude of the node What is a spin-orbit resonance (SOR) ? i: inclination M: mean anomaly : longitude of the periastron : rotation angle ε: obliquity φ: precession angle
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SOR of the 1 st kind (rotation)
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3/2 spin-orbit resonance (Mercury)
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Capture probability P cap ~ 7%
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Planetary perturbations
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Correia & Laskar, Nature, (2004)
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Irregular satellite Wisdom, Peale & Mignard, Icarus, (1984)
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Hyperion
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SOR of the 2 nd kind (precession)
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Ω
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Cassini states (~ 0º or ~ 180º) (0º 90º)
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Saturn Ward & Hamilton, AphJ, (2004) Boué et al., AphJ, (2009)
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Planetary perturbations
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Earth Laskar & Robutel, Nature, (1993)
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Venus Correia & Laskar, Nature, (2001)
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Hot-Jupiters Correia & Laskar, Exoplanets Book, (2010) Applications to Exoplanets
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Equilibrium Spin for Super-Earths Venus (aM = 0.723) GJ 581e (aM = 0.009) Arae c (aM = 0.101) Correia & Laskar, Exoplanets Book, (2010)
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Conclusions Hot-Jupiters are not likely to present rotation spin-orbit resonances neither high obliquity precession spin-orbit resonances. Super-Earths tidally evolved may present rotation spin-orbit resonances, in particular when found in eccentric orbits (as Mercury). The rotation may also be chaotic as Hyperion. Super-Earths may also present high obliquities (including retrograde configurations as Venus), or even chaotic spin orientation like Mars.
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“Spin-orbit resonances: our Solar System in context” Alexandre C.M. Correia (University of Aveiro) IAU Symposium 276, Turin, 14 th October 2010 Jacques Laskar (Paris Observatory)
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What is a resonance? + b=0 b small b large
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What is a resonance?
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Capture probability Goldreich & Peale, AphJ, (1966) P cap ~ 7%
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SOR of the 2 nd kind (precession) Ω
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Cassini states (~ 0º or ~ 180º) (0º 90º)
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