The problem, a bit more precisely, is that very small changes in the initial conditions can result in very large changes in result. So even if you have a perfec

The problem, a bit more precisely, is that very small changes in the initial conditions can result in very large changes in result. So even if you have a perfect numerical simulation, if your inputs are even slightly off the simulation might eventually be worthless. Unless you're in one of these islands of stability, maybe, I'm fuzzier on that. (And I don't know a lot about numerical simulation techniques, but I think that sort of situation also makes a "perfect" simulation even harder than usual.) Compare to two-body interactions, where there is a pretty small family of closed-form solutions to all the possible trajectories. You can just plug in a future time t and (in principle) get a mostly correct answer. In practice nothing is exactly two-body, the bodies aren't point masses, etc, but the small differences have proportionally small effects.