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 frame- work. Here the same model is extended by adding dissipative effects in the Earth{Moon system: the body tides and the fric- tion between the core and the mantle. Some constraints on the poorly known coefcients of dissipation are determined with the help of paleogeological observations. One consequence is that the scenario proposed by Williams (1993) for the past his- tory of the Earth's obliquity seems unlikely. A synthesis of 500 numerical integrations of the Earth{Moon system with orbital perturbationsforthenext5Gyrispresented.Itisshownthatthe 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 pos- sible evolutions conducted with a tidal dissipation coefcient 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. The evolution of the Earth{Moon system is far from being a new subject. Evidence of the loss of the Earth's angular mo-