Jacques Laskar and colleagues have been leaders in the field of long term solar system planetary motion calculations. Their earlier efforts have produced calculations of the solar system motions for more than 20 million years. These motions are important because they established that the 405,000 year earth ellipticity cycle can be used for more accurate dating of geological deposits.
Now they have extended their calculations to 60 million years and show that this is a limit. “Strong chaos induced by close encounters with Ceres and Vesta” by J. Laskar et al., Published in Astronomy & Astrophysics, 2011, vol. 532, L4.
A summary of this is presented in “When minor planets Ceres and Vesta rock the Earth into chaos“:
Although small, Ceres and Vesta gravitationally interact together and with the other planets of the Solar System. Because of these interactions, they are continuously pulled or pushed slightly out of their initial orbit. Calculations show that, after some time, these effects do not average out. Consequently, the bodies leave their initial orbits and, more importantly, their orbits are chaotic, meaning that we cannot predict their positions. The two bodies also have a significant probability of impacting each other, estimated at 0.2% per billion year. Last but not least, Ceres and Vesta gravitationally interact with the Earth, whose orbit also becomes unpredictable after only 60 million years. This means that the Earth’s eccentricity, which affects the large climatic variations on its surface, cannot be traced back more than 60 million years ago. This is indeed bad news for Paleoclimate studies. This unexpected discovery comes at a time when both objects are the targets of the NASA/Dawn mission. The Dawn probe will encounter Ceres in February 2015. At present, Dawn is approaching Vesta, and the flyby will occur on this coming Saturday, July 16, 2011.
For more, see the Wikipedia article on stability of the Solar System.
If astrophysics has been able to assist geology in dating deposits over a period of 20 million years, perhaps geology can return the favour by showing what were the actual Earth orbital motions beyond that time.