  We present the first dynamical solution of the triple asteroid system (45)
Eugenia and its two moons Petit-Prince (Diameter~7 km) and S/2004 (45) 1
(Diameter~5 km). The two moons orbit at 1165 and 610 km from the primary,
describing an almost-circular orbit (e~6x10-3 and e~7x10-2 respectively). The
system is quite different from the other known triple systems in the main belt
since the inclinations of the moon orbits are sizeable (9 deg and 18 deg with
respect to the equator of the primary respectively). No resonances, neither
secular nor due to Lidov-Kozai mechanism, were detected in our dynamical
solution, suggesting that these inclinations are not due to excitation modes
between the primary and the moons. A 10-year evolution study shows that the
orbits are slightly affected by perturbations from the Sun, and to a lesser
extent by mutual interactions between the moons. The estimated J2 of the
primary is three times lower than the theoretical one, calculated assuming the
shape of the primary and an homogeneous interior, possibly suggesting the
importance of other gravitational harmonics.
