Obliquity, precession rate, and nutation coefficients for a set of 100 asteroids^⋆

¹ Department of MathematicsUniversity of Rome Tor Vergata, 00133 Rome, Italy
² Observatoire de Paris, SYRTE/UMR-8630 CNRS, 75014 Paris, France
e-mail: Jean.Souchay@obspm.fr

Received: 31 January 2013
Accepted: 18 April 2013

Abstract

Context. Thanks to various space missions and the progress of ground-based observational techniques, the knowledge of asteroids has considerably increased in the recent years.

Aims. Due to this increasing database that accompanies this evolution, we compute for a set of 100 asteroids their rotational parameters: the moments of inertia along the principal axes of the object, the obliquity of the axis of rotation with respect to the orbital plane, the precession rates, and the nutation coefficients.

Methods. We select 100 asteroids for which the parameters for the study are well-known from observations or space missions. For each asteroid, we determine the moments of inertia, assuming an ellipsoidal shape. We calculate their obliquity from their orbit (instead of the ecliptic) and the orientation of the spin-pole. Finally, we calculate the precession rates and the largest nutation components. The number of asteroids concerned leads to some statistical studies of the output.

Results. We provide a table of rotational parameters for our set of asteroids. The table includes the obliquity, their axes ratio, their dynamical ellipticity H_d, and the scaling factor K. We compute the precession rate ψ̇ and the leading nutation coefficients Δψ and Δε. We observe similar characteristics, as observed by previous authors that is, a significantly larger number of asteroids rotates in the prograde mode (≈ 60%) than in the retrograde one with a bimodal distribution. In particular, there is a deficiency of objects with a polar axis close to the orbit. The precession rates have a mean absolute value of 18″/y, and the leading nutation coefficients have an average absolute amplitude of 5.7″ for Δψ and 5.2″ for Δε. At last, we identify and characterize some cases with large precession rates, as seen in 25143 Itokawa, with has a precession rate of about − 475′′/y.