Humility versus hubris - Does science have the potential to answer any question?

Okay, here’s just one question:

Where exactly will all the planets in our solar system be in 100,000 years from today May 27, 2009 at 5 pm GMT? We allow a margin of error of 10 feet.

The question is somewhat related to asking: Is the solar system stable or will one planet, say Mars, leave our solar system entering interstellar space?

What do you need to answer the question? Here are a couple of options. Please pick one:

1) A small personal computer and an astronomy program
2) A high-end computer with 16 processors
3) A data center full of high-end computers
4) A computer the size of Jupiter

Or does the question require a computer that consists of more than 10^85 atoms? If our universe is too small for that, does this mean science does not have the potential to answer any question?

Here’s the definition of the problem:

The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i.e., Newton’s laws of motion and Newton’s law of gravity.

http://en.wikipedia.org/wiki/N-body_problem

Any opinions?