> the computations would involve at least 10^8000000 terms.

Well we could speed up that simulation pretty easily, just arrange the actual masses and velocities somewhere...

Then I thought, is there a way to scale the distances, masses and velocities to create a system with the same, but proportionally faster behavior?

One guess as to perhaps why not: As distances get small, normal matter bodies will get close enough to actually collide. Perhaps some tiny primordial black holes would be useful.