First numerical ephemerides of the Martian moons

We present new ephemerides of Phobos and Deimos that are fit to observations from 1877 to 2005 and include recent spacecraft observations by Mars Global Surveyor and Mars Express. In contrast to earlier models, this is the first completely numerical one. In particular, the tidal effects have been modeled by the tidal bulge raised by each moon on the planet, instead of fitting secular accelerations in the satellite longitudes. This partly avoids absorbing the Deimos observational errors in its related tidal acceleration. Moreover, applying this model to other systems will be easier. Our estimate of the Martian dissipation is Q = 79.91±0.69 (1σ-formal error) when assuming $k_2 = 0.152$ for the Martian Love number and $G{m}_{\rm Ph}$ = 0.68$\times$106 m3/s2 for the Phobos mass. We also report the possibility of fitting the Phobos oblateness gravity field. We suspect a non-uniform density for Phobos or a bias in either the observations or the Martian gravity field. A FORTRAN subroutine that computes the Martian moons' ephemerides is available on request