A precise modeling of Phoebe’s rotation

¹ Observatoire de Paris, Systèmes de Référence Temps Espace (SYRTE), CNRS/UMR8630, Paris, France
e-mail: Laure.Cottereau@obspm.fr;Jean.Souchay@obspm.fr
² Main (Pulkovo) Astronomical Observatory of the Russian Academy of Sciences, Saint-Petersburg, Russia
e-mail: aek@gao.spb.ru

Received: 29 June 2010
Accepted: 13 August 2010

Abstract

Aims. Although the rotation of some Saturn’s satellites in spin-orbit has already been studied by several authors, this is not the case for the rotation of Phoebe, which stands out because it is non-resonant. The purpose of the paper is to determine for the first time and with precision its precession-nutation motion.

Methods. We adopt an Hamiltonian formalism of the rotation motion of rigid celestial bodies set up by Kinoshita (1977, Celest. Mech., 15, 277) based on Andoyer variables and canonical equations. First we calculate Phoebe’s obliquity at J2000,0 from available astronomical data as well as the gravitational perturbation caused by Saturn on Phoebe’s rotational motion. Then we carry out a numerical integration and compare our results for the precession rate and the nutation coefficients with a purely analytical model.

Results. Our results for Phoebe’s obliquity (23°95) and Phoebe’s precession rate (5580 ″̣65/cy) are very close to the respective values for the Earth. Moreover the amplitudes of the nutations (26′′ peak to peak for the nutaton in longitude and 8′′ for the nutation in obliquity) are on the same order as the respective amplitudes for the Earth. We give complete tables of nutation, obtained from a fast fourier transform (FFT) analysis starting from the numerical signals. We show that a purely analytical model of the nutation is not accurate because Phoebe’s orbital elements e, M and L_S do not show a simple linear behaviour at all.

Conclusions. The precession and nutation of Phoebe have been calculated for the first time in this paper. We will continue this study in the future by studying the additional gravitational effects of the Sun, of the large satellites such as Titan, as well as Saturn’s dynamical ellipticity.