Multiple asteroid systems (45) Eugenia and (87) Sylvia: Sensitivity to external and internal perturbations

Satellites of asteroids are a widely used way to determine the masses and other dynamical parameters of their systems. We make such a determination here, using data from the two triple-asteroid systems, (45) Eugenia and (87) Sylvia, that come from the Hubble Space Telescope and adaptive optics on three 8-10 m class telescopes (Keck, VLT, Gemini North). First, we determined what set of parameters can be precisely derived from a limited number of observations. Next, we deduced constraints on the inner structure of the main body of the systems. To do this, we fit our dynamical model ODIN to simulated observations to determine at what confidence level we can constrain the dynamical parameters. We deduced that the mass of the satellites is too small to be fitted with confidence, while the polar oblateness J2 of the primary can be constrained. Then, ODIN was fitted to observations of the systems to obtain the values of the polar oblateness J2. The difference between the theoretical value of J2, and our estimate deduced from the motion of the satellites, suggests that Eugenia is differentiated. We explore the properties needed by a dense and spherical core, surrounded by a less dense layer, to explain this difference. The lack of agreement between the different dynamical studies of Sylvia prevents us from making any definitive conclusion, but the large range of possible solutions points to an interesting inner structure.