I was reading about what is involved in making an ephemeris and wondered about this. Feeling I'd read pieces that extrapolated orbits over many thousands of years, I looked for an example and found this rather interesting one at phys.org:
Astronomy & Astrophysics is publishing a new study of the orbital evolution of minor planets Ceres and Vesta, a few days before the flyby of Vesta by the Dawn spacecraft. A team of astronomers found that close encounters among these bodies lead to strong chaotic behavior of their orbits, as well as of the Earth's eccentricity. This means, in particular, that the Earth's past orbit cannot be reconstructed beyond 60 million years.
The Wikipedia article on JPL's Development Ephemeris gives a sense of how tremendously complex these calculations are, and how many observations are used. This quote gives a bit of a sense:
DE418 was released in 2007 for planning the New Horizons mission to Pluto. New observations of Pluto, which took advantage of the new astrometric accuracy of the Hipparcos star catalog, were included in the fit. Mars spacecraft ranging and VLBI observations were updated through 2007. Asteroid masses were estimated differently. Lunar laser ranging data for the Moon was added for the first time since DE403, significantly improving the lunar orbit and librations. Estimated position data from the Cassini spacecraft was included in the fit, improving the orbit of Saturn, but rigorous analysis of the data was deferred to a later date. DE418 covered the years 1899 to 2051, and JPL recommended not using it outside of that range due to minor inconsistencies which remained in the planets' masses due to time constraints
How quickly does uncertainty creep into such calculations, and what sort of margin of error is involved? Does the computing ability of modern computers make a difference - that is, can all known objects and forces be entered into a program that crunches the numbers, or do the smaller things have to be dropped out of the formula? Does this affect mission planning to asteroids?