[dalke]

What part of "the whole Solar System possesses a Lyapunov time in the range of 2–230 million years" don't you agree with? Quote is from http://en.wikipedia.org/wiki/Stability_of_the_Solar_System .

To me it means that no matter how precise you measure everything, at some point even the unpredictability of a single atomic decay is enough to make a difference such that one of the planets may is ejected. As far as I know, that's also the generally accepted meaning.

[monochr]

Did you read your own link?

"In 1989, Jacques Laskar of the Bureau des Longitudes in Paris published the results of his numerical integration of the Solar System over 200 million years. These were not the full equations of motion, but rather averaged equations along the lines of those used by Laplace. Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time."

So yes, that's exactly what I said.

[dalke]

Would you clarify what it is you mean?

The observation you quoted isn't using the full equations of motion. The next study on that page uses a change of 1 meter and finds that 1% of the 2501 cases Mercury goes into a dangerous orbit, including one where "a subsequent decrease in Mercury’s eccentricity induces a transfer of angular momentum from the giant planets that destabilizes all the terrestrial planets ~3.34 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth."

You assert, seemingly as a matter of faith, that it is possible to measure all of the relevant factors such that a prediction can be made. We can't predict when an atom of uranium will decay, but we can make statistical predictions about the population. We can't predict when an air molecule out of a mole of molecule will hit the side of a bottle but we can make predictions about the pressure.

Do you think that we can ever do either of those two cases?

It's the same for the Solar System. As far as we can tell, it's not possible to have accurate enough information to predict the evolution of the Solar System. Even with numerical simulations, the presence of a space craft, or an extra-solar meteorite, might change things after 10 million years - things that can't be predicted.