Mapping the υ⊙ Secular Resonance for Retrograde Irregular Satellites

J. CORREA OTTO; A.M. LEIVA; C.A. GIUPPONE; C. BEAUGE

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

WILEY-BLACKWELL PUBLISHING, INC

Año: 2010 vol. 402 p. 1959 - 1968

0035-8711

Constructing dynamical maps from the filtered output of numerical integrations, we analyse the structure of the ν secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated with the secular angle θ = − , where is the longitude of the pericentre of the satellite and corresponds to the (fixed) planetocentric orbit of the Sun. Our study is performed in the restricted three-body problem, where thesatellites are considered as massless particles around a massive planet and perturbed by the Sun.Depending on the initial conditions, the resonance presents a diversity of possible resonant modes, including librations of θ around 0 (as found for Sinope and Pasiphae) or 180◦ as well asasymmetric librations (e.g. Narvi). Symmetric modes are present in all giant planets, although each regime appears restricted to certain values of the satellite inclination. Asymmetric solutions,on the other hand, seem absent around Neptune due to its almost circular heliocentric orbit.Simulating the effects of a smooth orbitalmigration on the satellite,we find that the resonance lock is preserved as long as the induced change in the semimajor axis is much slower comparedto the period of the resonant angle (adiabatic limit). However, the librational mode may vary during the process, switching between symmetric and asymmetric oscillations. Finally, we present a simple scaling transformation that allows us to estimate the resonantstructure around any giant planet from the results calculated around a single primary mass.