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“ 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” Universidade de Aveiro Philippe Robutel Alexandre C.M. Correia IMCCE / Observatoire de Paris gr@av group meetingMarch 5th, 2014 - Aveiro
Achilles “Chaotic Rotation in the Three-Body Coorbital Problem” Wolf (1906) stability: equilibrium: Lagrange (1772) Gascheau (1843)
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)
Two-Body Problem with Rotation Danby (1962)
Circular Orbits with Rotation Pendulum phase space:
Wisdom et al. (1984) Eccentric Orbits with Rotation Phobos Hyperion Mercury Moon Chirikov (1979)
Three-Body Coorbital Circular Problem (3BCP) Tadpole Horseshoe
Horseshoe Tadpole Co-rotating frame Érdi (1977)
3BCP with Rotation Correia & Robutel (2013)
Poincaré Sections ( = 1) = 0º = 10º = 50º Correia & Robutel (2013)
Poincaré Sections ( = 50º) log = 1.3 log = -0.4 log = 0.4 Correia & Robutel (2013)
Saturn Stability analysis Exo-Earths Correia & Robutel (2013)
log = 1.3 log = -0.4 log = 0.4 Tidal evolution ( = 50º) Correia & Robutel (2013)
= 0º = 10º = 50º Tidal evolution ( = 1) Correia & Robutel (2013)
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.