On the long term evolution of the spin of the Earth

Laskar and Robutel (1993) have globally analyzed the stability of the planetary obliquities in a conservative framework. Here the same model is extended by adding dissipative effects in the Earth-Moon system: the body tides and the friction between the core and the mantle. Some constraints on the poorly known coefficients of dissipation are determined with the help of paleogeological observations. One consequence is that the scenario proposed by Williams (1993) for the past history of the Earth's obliquity seems unlikely. A synthesis of 500 numerical integrations of the Earth-Moon system with orbital perturbations for the next 5 Gyr is presented. It is shown that the time scale of the dissipative effects is long enough to induce an adiabatic-like evolution of the obliquity which is driven in the chaotic zone within 1.5 to 4.5 Gyr. A statistical study of possible evolutions conducted with a tidal dissipation coefficient Delta t of 600 seconds demonstrated that 68.4% of the trajectories attained an obliquity larger than 81 degrees, with a maximum of 89.5 degrees.