This isn’t true. We have very reliable libraries for simulating N-body problems to sufficient detail to know the answers to such questions with great certainty.

This isn’t true. We have very reliable libraries for simulating N-body problems to sufficient detail to know the answers to such questions with great certainty. Not having an “exact solution” Does not bound whether solutions exist or whether they are computable, or how easy they are to compute. In this case, quite easy.