How to calculate planetary position over vast time spans Ignoring the turbulent beginnings of our solar system I wonder if there is a meaningful way to calculate the relative position of the planets of our solar system 100 million years into the future using the standard parameters 
N /  i  /  w /  a /  e   /  M / +- pertubations , {assuming no unannounced black hole or neutron star zips through our solar system in the meantime.} 
How far can the orbital calculations be projected into the future before error accumulation make these calculations completely meaningless?
Jacques Laskar, at IMCCE, has been working on describing planetary motions on long term time scales.

Quoting and translating a paper by him:


Motion in the solar system is chaotic, meaning that trajectories diverge exponentially: an error on the location of a planet gets multiplied by 10 every 10 million years
This means that a 15 meter error on the initial location of the Earth yields an error of 150 meters after 10 million years, and 150 million km afer 100 million years. Long term predictions involving a single trajectory are impossible.


For predictions over longer periods, it becomes necessary to study multiple possible trajectories. Laskar and Gastineau have published results of a simulation of the solar system involving 2501 variations of the location of Mercury. In this simulation, "initial conditions  differ by only 0.38 mm in the semi-major axis of Mercury". Some of those trajectories involve "possible collisions of Mercury, Mars or Venus with the Earth".