Geologic constraints on the chaotic diffusion of the solar system

The correlation of Earth's orbital parameters with climatic variations has been used to generate astronomically calibrated geologic time scales of high accuracy. However, because of the chaotic behavior of the solar system, two initially close calculations of Earth's orbit diverge exponentially and have a large uncertainty beyond several million years in the past. This chaotic behavior is related to a combination of angles in the precession motion of the orbits of Earth and Mars, theta, which currently is in resonance. How long theta stays in libration critically depends on the dynamical model and initial conditions for the solar system. Here we show that geologic data can differentiate between astronomical solutions that do and do not exhibit a transition in theta since 40 Ma and that sediments can thus provide a history for the evolution of theta. We find that the chaotic transition of theta from libration to circulation did not occur after ca. 30 Ma. We can thus constrain the chaotic diffusion of the solar system in the past, and our results provide new and challenging constraints for astronomical models.