The Orbits and Masses of the Martian Satellites and the Libration of Phobos

This paper reports on an update to the orbits and masses of the Martian satellites Phobos and Deimos. We obtained the orbits by fitting a numerical integration to all available Earth-based astrometry through the opposition of 2003, spacecraft imaging observations through 2007, and the Doppler tracking of the Viking and Phobos 2 spacecraft; the Doppler data provide information on the satellite masses. Our dynamical model included the figure acceleration due to a librating Phobos; we determined the amplitude of the forced libration. We also took into account the secular acceleration of Phobos due to the tide that it raises on Mars and estimated the Martian tidal quality factor Q. We provide an assessment of the accuracy of the orbits and a geometrical description of the orbits in the form of mean elements.