Orbital evolution and origin of the Martian satellites

Abstract

The role of tidal dissipation within the Martian satellite system is examined through orbital evolution integrations and assessed in the context of its origin scenario through calculations of collision probabilities between Phobos and Deimos in the distant past. A wide range of assumptions concerning models of dissipation by anelastic tidal deformation within Mars and its satellites has been considered in investigating the possibility of a capture origin using generalized Q laws and the Darwin-Kaula formulation of the secular evolution equations. The integration of the equations of evolution confirms a previous finding (P. Goldreich, Mon. Not. Roy. Astron. Soc. 126, 257–268, 1963; S. F. Singer, Trans. Amer. Geophys. Union 51, 637–641, 1970; K. Lambeck, J. Geophys. Res. 84, 5651–5658, 1979) that Deimos in its present form could not have been captured. Calculations of collision probabilities provide further evidence against a capture origin, for if Phobos and Deimos were captured, they would most probably have collided at some stage. It seems reasonable to assume that a collision event would not have resulted in a highly regular Deimos orbit, even though Phobos could have been tidally evolved to its present orbit after a collision. An accretion origin is therefore preferred over capture, although an accretion model that is consistent with the likely carbonaceous chondritic composition of the Martian satellites has yet to be established. Constraints on the Q laws of Phobos can then be established on the assumption that a collision between Phobos and Deimos has not occurred in the past 1.5 billion years or longer, as indicated by their exposure ages (J. Veverka, Vistas Astron. 22, 163–192, 1978).