You can't solve the problem analytically for n>=3. That is to say, you cannot solve the whole thing mathematically so that you get an exact function

r(t)

(place as a function of time, say)

for all n bodies.
Of course, nothing stops us to approximate (even to excellent precision) their paths, as for instance you did in your simulation (though I'd guess we can reach higher precision than your simulation did :)). But it is not perfect and exact, and over large timescales, you will see that your simulated prediction will differ to what you'd see in nature.


Does that answer your question?