Rotational motion of Phobos

¹ Université Pierre et Marie Curie, UPMC, Paris 06, France
² IMCCE, Observatoire de Paris, CNRS UMR 8028, 77 avenue Denfert-Rochereau, 75014 Paris, France
e-mail: Nicolas.Rambaux@imcce.fr
³ Jet Propulsion Laboratory, Caltech, Pasadena, USA
e-mail: julie.c.castillo@jpl.nasa.gov
⁴ Royal Observatory of Belgium, 3 Avenue Circulaire, 1180 Brussels, Belgium
e-mail: rosenb@oma.be; s.maistre@oma.be

Received: 29 May 2012
Accepted: 10 September 2012

Abstract

Context. Phobos is in synchronous spin-orbit resonance around Mars, like our Moon around the Earth. As a consequence, the rotational period of Phobos is equal in average to its orbital period. The variations of its rotational motion are described by oscillations, called physical librations, which yield information of its interior structure. The largest libration of Phobos rotational motion was first detected in 1981 and the determination of this libration has recently been improved using Mars EXpress observations.

Aims. The objective of this paper is to present the spectrum of Phobos’ librations by using recent orbital ephemerides and geophysical knowledge of this Martian satellite. The analysis of the librational spectrum highlights the relationship between dynamical and geophysical properties of the body, but is also useful for cartographic and geodetic purposes for future space missions dedicated to Phobos.

Methods. We developed a numerical model of Phobos’ rotation that includes the point-mass Mars acting on the dynamical shape of Phobos, expanded to the third degree, and the effect of Mars’ oblateness. The forced librations spectrum is extracted through a frequency analysis.

Results. We find that the libration in longitude presents a quadratic term that coincides with the secular acceleration of Phobos falling onto Mars. The primary libration in longitude has a period equal to the anomalistic mean motion, whereas the primary libration in latitude has a period equal to the draconic mean motion (node to node). Both librations have amplitudes of about one degree leading to a surface displacement of about 200 m. These two components dominate the libration spectrum by a factor one hundred. Phobos’ third degree gravity harmonics and Mars’ oblateness affect the librations amplitude at 10^-4 degree. This is small but detectable from long-term tracking of a lander. The determination of the librational spectrum would bring strong constraints on the principal torques acting on the Martian moon, as well as on the possible presence of lateral variations in density predicted by certain geophysical models of the Stickney crater formation. We also investigate the obliquity variations of Phobos and find that their amplitudes are larger than the mean value of the obliquity.

Conclusions. Phobos exhibits a rich and varied set of librational oscillations. The main librations and the librations close to the proper frequencies are the most sensitive to the interior structure. On the other hand, the superimposed effect of large amplitude oscillations is likely to make the determination of the mean obliquity challenging.