Asteroids with satellites are natural laboratories to constrain the formation and evolution of our solar system. The binary Trojan asteroid (624) Hektor is the only known Trojan asteroid to possess a small satellite. Based on W.M. Keck adaptive optics observations, we found a unique and stable orbital solution, which is uncommon in comparison to the orbits of other large multiple asteroid systems studied so far. From lightcurve observations recorded since 1957, we showed that because the large R eq =125-km primary may be made of two joint lobes, the moon could be ejecta of the low-velocity encounter, which formed the system. The inferred density of Hektor's system is comparable to the L5 Trojan doublet (617) Patroclus but due to their difference in physical properties and in reflectance spectra, both captured Trojan asteroids could have a different composition and origin.2 1. INTRODUCTION As of today ~200 asteroids are known to possess one or several satellites across all populations of small solar system bodies (Richardson and Walsh, 2006), from the near-earth asteroids (Pravec et al. 2006), to the asteroid main-belt beyond (Noll et al. 2008). Their existence and the study of their mutual orbits lead to significant constraints on the formation of our solar system through the determination of the mass, densities, mass ratio and long term evolution of the system. In the Jupiter Trojan population, (617) Patroclus is the only doublet asteroid systems, made of two comparable-sized components, which has been imaged and studied so far (Marchis et al. 2006b). We report in this work on the shape and interior of the L4 multiple Trojan (624) Hektor and on the analysis of the orbit of its moon based on our AO observations and additional datasets. We discuss the internal structure of the primary in comparison with the one of another binary Trojan asteroid (617) Patroclus.

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion or when the satellite will circulate with respect to the primary. We find the existence of stable equilibrium points about which the satellite can librate, and explore both the linearized and non-linear dynamics around these points. Absolute bounds are placed on the phase space of the libration-orbit coupling through the use of zero-velocity curves that exist in the system. These zerovelocity curves are used to derive a sufficient condition for when the satellite's libration is bound to less than 90 • . When this condition is not satisfied so that circulation of the satellite is possible, the initial conditions at zero libration angle are determined which lead to circulation of the satellite. Exact analytical conditions for circulation and the maximum libration angle are derived for the case of a small satellite in orbits of any eccentricity.