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Good evening everyone, since Poincaré demonstrated that there are no exact solutions to the Three-body problem, many scientists have developed techniques to approximate these solutions.

The Newtonian approach has been well studied so far, and if I understand correctly the relativistic approach is not really the best because General Relativity is not an N-body theory but rather a field theory.

I read that the numerical simulations of this problem are very accurate nowadays but that many of the solutions found are very unstable in reality.

  • Can we consider today that this problem has been sufficiently explored ? and should we spend more time on the N-body problem ?
  • Or should we continue to deepen our knowledge of this problem ?
  • If so, what are the aspects of this problem that are unexplored or not well understood?

I hope my questions are not too vague. If that's the case, let me know and I'll rephrase them.

Loïc Poncin
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Sure, many papers have been put out on the three-body problem in recent years, like this one and this one. It's a nice example of a chaotic system that's still reasonably tractable (as chaotic systems go), so there's probably still stuff to be learned from it. Just in past few decades, people have found exact solutions to the few-body problem with really counterintuitive behavior - for example, a five-body system where one particle's velocity diverges to infinity in finite time without colliding with any of the other particles.

tparker
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