One of the best astronomy books I ever read is "Newton's Clock: Chaos Theory in the Solar System." This, both for its detailed and insightful history of astronomy, and for a "mild" presentation of chaos theory as it is related to planetary, asteroidal, and cometary orbits.
Basically, and I don't want to "defend" it here, but orbital calculations are pretty precise --to the limit of how far down the chain of differential equations required that you want to (or can) go.
Regardless of the enormous computing power available today, there is still a limit on this. And it has been demonstrated that occasionally, that last-plus-one differential term that you didn't evaluate, does make a difference either suddenly or over the long term.
Thus, we can never know for sure whether or not a tiny unpredicted impact of a one pound object with another one-pound object out by Pluto will ultimately disrupt the orbital mechanics of the whole solar system. Far-fetched, but so is getting an ace-high straight flush.
Yes, within the rather incredibly sophisticated and detailed orbital calculations of the major solar bodies, everything looks OK for the next 10^X years. But there are innumerable little chunks of ice and rocks out there, beyond the asteroid belt, which interact with each other in unknown ways.
Take a look at the rings of Saturn. In the flybys, it was noted that the small bodies which comprise them are actually orbiting each other, such that within each ring, they have formed up into complex spiral orbits within the ring itself. This was pretty much unexpected, and their interactions are still ongoing.
Astronomers have a hard enogh time calculating the orbit of the moon, and as of about 1996, they finally got it to within two or three seconds of arc. But as far as I know, that's about the best we know.
Pretty good, huh? But remember, almost every spectacular space shot we make, to the moon or Mars or to that comet we plunked with an 800 lb copper slug, took mid-course corrections.
For centuries, astronomers have dealt with what is called the "Three-Body Problem," that is, to calculate the orbits of three bodies swinging around each other. We've got that down pretty pat now, with our supercomputers and all.
But with the realities of the solar system, we're not dealing with three bodies. We're dealing with "The Million-Body" problem.
So how nigh is nigh? Nobody really knows for sure.
You just play the cards you have in your hand. You takes your chances, and you makes your bet.
Terry
