Evolution of the Martian satellites

The tidal evolution of both Martian satellites is investigated for a frequency dependent model of the tidal lag. The dissipation within the planet and the satellite are simultaneously taken into account and various assumptions are made of their respective importance. Because of the solar perturbation, we have referred the orbit of Phobos to the Laplacian plane of the system whose determination for large eccentricity is found. If the present secular acceleration is representative of the past situation, the orbit of Phobos has possibly evolved from one of high eccentricity some billions of years ago. The dissipation within the satellite appears as a critical parameter to discriminate between the different scenarios. For a weak dissipation we find that the inclination to the equator of Mars has not changed much in the past 4.5 × 109 yr, Phobos orbiting Mars at about 7 to 10 planetary radii at its origin, its eccentricity being 0.6; whereas in the case of important dissipation the semi-major axis could have been greater than 20 radii, the satellite lying between the ecliptic and the equator in a highly eccentric orbit. The time required to move Deimos far from its present orbit is much greater than the age of the Solar System and we conclude that it has not undergone a tidal evolution. Finally, the two most popular theories for the origin of the Martian satellites are briefly reviewed in the light of our results and we show that the usual objection to capture, the inclination problem, is weakened as far as Phobos is concerned.