These wacky looking planetary orbits arise when you start considering the gravitational force between n>2 planets • No closed form solution is known for n>2, and is known as the n-body problempic.twitter.com/581Canf5OP
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There are no “closed form” solutions for two black holes, so everything is done by numerical simulation, I believe. That’s why detecting gravitational waves from black holes is not really an “exact” science yet. You have to use a lot of statistics and numerical modeling.
Just because the closed form doesn’t exist doesn’t mean the laws aren’t exact, and we can obtain results to arbitrary precision
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There is no “Final Theory” in Physics (yet). Newton’s laws, just like GR are still approximations. For example, physicists are still looking for a theory that contains GR and quantum field theory. Near black holes, quantum effects become important. “Precision is relative”(sic)!
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