“ chaotic rotation in the three-body coorbital problem ”
DESCRIPTION
“ 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). - PowerPoint PPT PresentationTRANSCRIPT
““Chaotic Rotation in the Chaotic Rotation in the Three-Body Coorbital ProblemThree-Body Coorbital Problem””
Alexandre C.M. Alexandre C.M. CorreiaCorreia
IMCCE / Observatoire de IMCCE / Observatoire de ParisParis
gr@av group meetinggr@av group meetingMarch 5March 5thth, 2014 - Aveiro , 2014 - Aveiro
Philippe RobutelPhilippe Robutel
Universidade de AveiroUniversidade de Aveiro
““Chaotic Rotation in the Chaotic Rotation in the Three-Body Coorbital ProblemThree-Body Coorbital Problem””
equilibrium:Lagrange
(1772)
Gascheau (1843)
Wolf (1906)Achilles
stability:
a: semi-major axis
e: eccentricity
ω: longitude of the perihelion
λ: mean anomay
λ
λ = λ0 + n (t – t0)
Two-Body Problem (Kepler problem)Two-Body Problem (Kepler problem)
ω
Two-Body Problem with Two-Body Problem with RotationRotation
Danby (1962)
Circular Orbits with Circular Orbits with RotationRotation
Pendulum phase space:
Eccentric Orbits with Eccentric Orbits with RotationRotation
Eccentric Orbits with Eccentric Orbits with RotationRotation
Phobos Mercury
Moon
Hyperion
Wisdom et al. (1984)
Chirikov (1979)
Three-Body Coorbital Three-Body Coorbital Circular Problem (Circular Problem (3BCP)3BCP)
Tadpole
Horseshoe
Co-rotating frameCo-rotating frame
Tadpole
Horseshoe
Érdi (1977)
3BCP with 3BCP with RotationRotation
Correia & Robutel (2013)
PoincarPoincaré Sections (é Sections ( = 1 = 1))
= 0º = 50º = 10º
Correia & Robutel (2013)
PoincarPoincaré Sections (é Sections ( = 50º = 50º))
log = 1.3
log = 0.4
log = -0.4
Correia & Robutel (2013)
Stability analysisStability analysisSaturnSaturn
Exo-EarthsExo-Earths
Correia & Robutel (2013)
Dissipation & CaptureDissipation & Capture
Tidal evolutionTidal evolution ( ( = 50º = 50º))log =
1.3log =
0.4log = -
0.4
Correia & Robutel (2013)
Tidal evolutionTidal evolution ( ( = 1 = 1)) = 0º = 50º = 10º
Correia & Robutel (2013)
Conclusions: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.