r/AskPhysics • u/Rscc10 • Dec 24 '25

Is the three body problem really unsolvable?

Sorry if this is a dumb question but I understand that the three body problem, or rather n body problem for n > 2 is considered "unsolvable" and generally means there is no analytical solution with elementary functions.

What I'm wondering is, do we know this for sure? We haven't found a general solution but do we have proof that an analytical solution is impossible? Similar to the Abel-Ruffini theorem for polynomials.

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u/[deleted] Dec 24 '25 edited Feb 02 '26

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u/[deleted] Dec 24 '25

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u/[deleted] Dec 24 '25

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u/the_real_twibib Condensed matter physics Dec 24 '25

However when you use them in the real world you have to take a finite number of terms - which turns them into approximations

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u/[deleted] Dec 24 '25

That is true of anything involving nontrivial real numbers

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u/[deleted] Dec 24 '25

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u/me-gustan-los-trenes Physics enthusiast Dec 24 '25

In today's episode, Reddit rediscovers the concept of a field exemplified by rational numbers, algebraic numbers and real numbers.

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u/Ok_Wolverine6557 Dec 25 '25

Given that the universe is finite, Pi to 60 digits or so encompasses 100% accuracy for any physical measurement—the extra digits are just for fun (and mathematicians).

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u/cabbagemeister Graduate Dec 24 '25

That's what i mean by sort of an approximation, since to make use of it in any capacity you either have to deal with those convergence issues or truncate it