For a two-body problem computing a future location in spacetime of the two bodies is easy enough -- easy with Newtonian gravity, and a bit harder with General R

For a two-body problem computing a future location in spacetime of the two bodies is easy enough -- easy with Newtonian gravity, and a bit harder with General Relativity. For an N-body problem, with N>2 there are no formulas that can give you the answer, and instead you have to do a numerical computation using as small a dt (ideally an infinitesimal time step) as possible, with as much precision as possible, and as many steps as needed to get to that future point in time. Obviously the numerical computation will a) take time, b) have errors (due to not having infinite precision and true infinitesimals). Apart from that the N-body problem is chaotic anyways.