Evolution of the Earth obliquity after the tidal expansion of the Moon orbit

The evolution of the Earth obliquity when the tidal interactions of the Earth-Moon system will have expanded the lunar orbit to about 66 and 68 Earth radii is studied. By integrating numerically the differential precession equations for the spin axis of the Earth, it is found that the evolution of the obliquity becomes chaotic due to the resonance overlapping of some Solar System fundamental frequencies. These frequencies have been identified as the s3, s4 and s6 in Laskarʹs solution (Laskar, Astron. Astrophys., 198, 341, 1988).