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New astrometric reductions of the US Naval Observatory CCD Astrograph Catalog (UCAC) all-sky observations were performed from first principles using the TGAS stars in the 8 to 11 magnitude range as reference star catalog. Significant improvements in the astrometric solutions were obtained and the UCAC5 catalog of mean positions at a mean epoch near 2001 was generated. By combining UCAC5 with Gaia DR1 data new proper motions on the Gaia coordinate system for over 107 million stars were obtained with typical accuracies of 1 to 2 mas/yr (R = 11 to 15 mag), and about 5 mas/yr at 16th mag. Proper motions of most TGAS stars are improved over their Gaia data and the precision level of TGAS proper motions is extended to many millions more, fainter stars. External comparisons were made using stellar cluster fields and extragalactic sources. The TGAS data allow us to derive the limiting precision of the UCAC x, y data, which is significantly better than 1/100 pixel.

Although it is accepted that the significant eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin-orbit resonance, open are the questions of how exactly and when the capture took place. A recent work by Makarov (2012) has demonstrated that trapping into this resonance is certain if the eccentricity is larger than 0.2 , provided that we use a realistic tidal model, the one which is based on the Darwin-Kaula expansion of the tidal torque.

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Perturbations of all sorts destabilise the rotation of a small body and leave it in a non-principal spin state. In such a state, the body experiences alternating stresses generated by the inertial forces. This yields nutation relaxation, i.e., evolution of the spin towards the principal rotation about the maximal-inertia axis. Knowledge of the timescales needed to damp the nutation is crucial in studies of small bodies' dynamics. In the literature hitherto, nutation relaxation has always been described with aid of an empirical quality factor Q introduced to parameterise the energy dissipation rate.Among the drawbacks of this approach was its inability to describe the dependence of the relaxation rate upon the current nutation angle. This inability stemmed from our lack of knowledge of the quality factor's dependence on the forcing frequency. In this article, we derive our description of nutation damping directly from the rheological law obeyed by the material. This renders us the nutation damping rate as a function of the current nutation angle, as well as of the shape and the rheological parameters of the body. In contradistinction from the approach based on an empirical Q -factor, our development gives a zero damping rate in the spherical-shape limit. Our method is generic and applicable to any shape and to any linear rheological law. However, to simplify the developments, here we consider a dynamically oblate rotator with a Maxwell rheology.Key words: minor planets, asteroids: general -celestial mechanics -methods: analytical 1 MOTIVATION Prendergast (1958) and, later, Burns (1971 drew attention to the fact that alternating dissipative forces emerging in a precessing rotator must reduce its kinetic energy without affecting its angular momentum. With no external torques acting on the body, its nonprincipal rotation must relax to motion about the maximal-inertial axis -a spin state corresponding to the minimal energy with a fixed angular momentum. The then available statistics on asteroids contained only singly-periodic curves, warranting that all the observed asteroids were in the final spin state.In the turbulent antecedents of the solar system, there were aeons when collisions and disruptions were regular, so asteroids (and their smithereens) were set into wobble often. Even in the present epoch, there happen events capable of kicking asteroids out of principal spin. Such events include occasional collisions, as well as tidal interactions during asteroids' close flybys near planets. Small bodies can be ⋆ Contact e-mail: julien.frouard.ctr@navy.mil † Contact e-mail: michael.efroimsky@navy.mil driven into nonprincipal axis (NPA) spin also by the YORP effect -see, e.g., Vokrouhlický et al. (2007) and Breiter, Rożek & Vokrouhlický (2011) and references therein. Wobble of comets is impelled mainly by jetting. Gradual outgassing, too, may contribute to the effect, because a rotator goes into tumbling when it changes its principal axes through a partial loss or redistribution of the material.In an excited...