The limits of Earth orbital calculations for geological time-scale use

The orbital motion of the planets in the Solar System is chaotic. As a result, initially close orbits diverge exponentially with a characteristic Lyapunov time of 5 Ma. This sensitivity to initial conditions will limit the possibility to obtain an accurate solution for the orbital and precessional motion of the Earth over more than 35 to 50 Ma. The principal sources of uncertainty in the model are review here. It appears that at present the largest source of error could reside in the lack of knowledge of the value of the precession due to the oblateness (J2) of the Sun. Nevertheless, for the calibration of geological time-scale, this limitation can be overcome to some extent if one considers in the geological data the signature of the outer planets secular orbital motion which is predictable on a much longer time-scale. Moreover, it should be possible to observe in the geological records the trace of transition from the (s4 −s3)−2(g4− g3) secular resonance to the (s4− s3)− (g4− g3) resonance. The detection and dating of these passages should induce extremely high constraints on the dynamical models for the orbital evolution of the Solar System.