Rotational motion of Vesta
Résumé
Vesta is the second most massive body of the asteroid belt and contains a giant impact and a differentiated interior. Constraints on internal structure can be inferred from various observations such as gravity field measurements [1]. Especially, detailed knowledge of the rotational motion can help constrain the mass distribution inside the body, which in turn can lead to information on its history. Here, we compute the polar motion, precession-nutation, and length-of-day variations of Vesta. The Vesta's Pole position in space has been obtained by Dawn mission [1] and the orbital pole of Vesta at J2000 can be obtained from the Horizons ephemerides [2]. The obliquity, defined as the angle between the normal to the orbital plane and the figure axis, brings information on the moment of inertia if it has reached its equilibrium position [3], the present value from observations is around 27 degrees. That is far from the 0.03 deg expected for the equilibrium position. In addition, the required timescale to fully damped the obliquity appears to be very long following the same approach developed in [4]. Thus, it appears that the obliquity of Vesta has not yet relaxed in its Cassini state. The figure of Vesta appears to be triaxial and the Sun exerts a non-zero torque. By following the approach developed for the Earth [e.g. 5] and Ceres [4], we compute the nutation of Vesta. The nutational motion of Vesta is dominated by the semi-annual nutation (996 milli-arcseconds or 1.26 m surface displacement) related to the large obliquity of Vesta, and then terms related to harmonics and also to the planet's mean longitude. The detection of such small displacement requires tracking of Vesta's surface with high precision. The precession time of the axis of Vesta is very long, about 179,000 years.