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The Cassini spacecraft collects high resolution images of the saturniansatellites and reveals the surface of these new worlds. The shape and rotationof the satellites can be determined from the Cassini Imaging Science Subsystemdata, employing limb coordinates and stereogrammetric control points. This isthe case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of newrotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).Especially, Epimetheus is characterized by its horseshoe shape orbit and thepresence of the swap is essential to introduce explicitly into rotationalmodels. During its journey in the saturnian system, Cassini spacecraftaccumulates the observational data of the other satellites and it will bepossible to determine the rotational parameters of several of them. To preparethese future observations, we built rotational models of the coorbital (alsocalled Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in additionto Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 andL_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbitalof Dione. The goal of this study is to understand how the departure from theKeplerian motion induced by the perturbations of the coorbital body, influencesthe rotation of these satellites. To this aim, we introduce explicitly theperturbation in the rotational equations by using the formalism developed byErdi (1977) to represent the coorbital motions, and so we describe therotational motion of the coorbitals, Janus and Epimetheus included, in compactform.

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn