“Spin-orbit resonances: our Solar System in context” Alexandre Correia (University of Aveiro / Paris Observatory) IAU Symposium 276, Turin, 14 th October.

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Presentation transcript:

“Spin-orbit resonances: our Solar System in context” Alexandre Correia (University of Aveiro / Paris Observatory) IAU Symposium 276, Turin, 14 th October 2010

What is a spin-orbit resonance (SOR) ?  : rotation angle ε: obliquity φ: precession angle

 : longitude of the node ω Ω What is a spin-orbit resonance (SOR) ? i: inclination M: mean anomaly  : longitude of the periastron

 : 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

SOR of the 1 st kind (rotation)

3/2 spin-orbit resonance (Mercury)

Capture probability P cap ~ 7%

Planetary perturbations

Correia & Laskar, Nature, (2004)

Irregular satellite Wisdom, Peale & Mignard, Icarus, (1984)

Hyperion

SOR of the 2 nd kind (precession)

Ω

Cassini states (~ 0º or ~ 180º) (0º  90º)

Saturn Ward & Hamilton, AphJ, (2004) Boué et al., AphJ, (2009)

Planetary perturbations

Earth Laskar & Robutel, Nature, (1993)

Venus Correia & Laskar, Nature, (2001)

Hot-Jupiters Correia & Laskar, Exoplanets Book, (2010) Applications to Exoplanets

Equilibrium Spin for Super-Earths Venus (aM = 0.723) GJ 581e (aM = 0.009)  Arae c (aM = 0.101) Correia & Laskar, Exoplanets Book, (2010)

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.

“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)

   What is a resonance? + b=0 b small b large

What is a resonance?

Capture probability Goldreich & Peale, AphJ, (1966) P cap ~ 7% 

SOR of the 2 nd kind (precession) Ω

Cassini states (~ 0º or ~ 180º) (0º  90º)