Gravity field and solar component of the precession rate and nutation coefficients of Comet 67P/Churyumov-Gerasimenko

Abstract

The aim of this study is first to determine the gravity field of the comet 67P/Churyumov-Gerasimenko and second to derive the solar component of the precession rate and nutation coefficients of the spin-axis of the comet nucleus, i.e. without the direct, usually larger, effect of outgassing. The gravity field and related moments of inertia are obtained from two polyhedra, which are provided by the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) and NAVigation CAMera (NAVCAM) experiments on Rosetta, and are based on the assumption of uniform density for the comet nucleus. We also calculate the forced precession rate as well as the nutation coefficients on the basis of Kinoshita's theory of rotation of the rigid Earth and adapted it to be able to indirectly include the effect of outgassing on the rotational parameters. The second degree denormalized Stokes coefficients of comet 67P/C-G turn out to be (bracketed numbers refer to second shape model) C20 ≃ -6.74 [-7.93] × 10-2, C22 ≃ 2.60 [2.71] × 10-2, consistent with normalized principal moments of inertia A/MR2 ≃ 0.13 [0.11], B/MR2 ≃ 0.23 [0.22], with polar moment c = C/MR2 ≃ 0.25, depending on the choice of the polyhedron model. The obliquity between the rotation axis and the mean orbit normal is ε ≃ 52°, and the precession rate only due to solar torques becomes ψ ε [20, 30] arcsec yr-1. Oscillations in longitude caused by the gravitational pull of the Sun turn out to be of the order of Δψ ≃ 1 arcmin, and oscillations in obliquity can be estimated to be of the order of Δε ≃ 0.5 arcmin.