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“ Chaotic Rotation in the Three-Body Coorbital Problem ”

“ Chaotic Rotation in the Three-Body Coorbital Problem ”. Universidade de Aveiro. Philippe Robutel. Alexandre C.M. Correia. IMCCE / Observatoire de Paris. gr@av group meeting March 5 th , 2014 - Aveiro. Achilles. “ Chaotic Rotation in the Three-Body Coorbital Problem ”. Wolf (1906).

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“ Chaotic Rotation in the Three-Body Coorbital Problem ”

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  1. “Chaotic Rotation in the Three-Body Coorbital Problem” Universidade de Aveiro Philippe Robutel Alexandre C.M. Correia IMCCE / Observatoire de Paris gr@av group meetingMarch 5th, 2014 - Aveiro

  2. Achilles “Chaotic Rotation in the Three-Body Coorbital Problem” Wolf (1906) stability: equilibrium: Lagrange (1772) Gascheau (1843)

  3. Two-Body Problem (Kepler problem) λ a: semi-major axis e: eccentricity ω: longitude of the perihelion λ: mean anomay ω λ = λ0 + n (t – t0)

  4. Two-Body Problem with Rotation Danby (1962)

  5. Circular Orbits with Rotation Pendulum phase space:

  6. Eccentric Orbits with Rotation

  7. Wisdom et al. (1984) Eccentric Orbits with Rotation Phobos Hyperion Mercury Moon Chirikov (1979)

  8. Three-Body Coorbital Circular Problem (3BCP) Tadpole Horseshoe

  9. Horseshoe Tadpole Co-rotating frame Érdi (1977)

  10. 3BCP with Rotation Correia & Robutel (2013)

  11. Poincaré Sections ( = 1)  = 0º  = 10º  = 50º Correia & Robutel (2013)

  12. Poincaré Sections ( = 50º) log = 1.3 log = -0.4 log = 0.4 Correia & Robutel (2013)

  13. Saturn Stability analysis Exo-Earths Correia & Robutel (2013)

  14. Dissipation & Capture

  15. log = 1.3 log = -0.4 log = 0.4 Tidal evolution ( = 50º) Correia & Robutel (2013)

  16.  = 0º  = 10º  = 50º Tidal evolution ( = 1) Correia & Robutel (2013)

  17. Conclusions: • Coorbital bodies in quasi-circular orbits may present chaotic rotation for a wide range of mass ratios and body shapes. • We show the existence of an entirely new family of spin-orbit resonances at the frequencies n  k/2. • The rotational dynamics of a body cannot be dissociated from its orbital environment.

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