The rotational motion of Vesta

Context. Vesta is the second largest body of the main asteroid belt, and it has been studied recently in great detail by the Dawn mission. It was the first time that this asteroid, or protoplanet, has been explored by a space mission, and it revealed a differentiated body. The knowledge of the rotational motion and, especially, its precession-nutation and length-of-day variations may add precious information on its interior. Aims. The objective of this paper is to present the first rotational model of Vesta based on the data acquired by the Dawn mission. The Dawn mission determined the orientation of Vesta with 0.01 degree accuracy, as well as the second degree of the gravity coefficients with a few percent accuracy [Russell et al. 2012]. Methods. We built a semi-analytical model of the rotational motion of Vesta based on the orbital perturbations and the large triaxial shape of Vesta. The rotational motion is then described through the polar motion, precession, nutation, and length-of-day variations. The sensitivity of the precession-nutation is given as a function of the polar moment of inertia, which has not yet been determined. Results. We find that the amplitude of the nutation is about 2000 milli-arcseconds at the semi-annual period, whereas the amplitude of the length-of-day variation is about 3 mas/days, in the semi-diurnal period. Finally, we show that the signature of the polar moment of inertia, which is crucial for constraining geophysical model, is on the order of 200 milli-arcseconds for the semi-annual nutations for two extrema of polar moment with inertia values of 0.38-0.42.