There is a series solution to the 3-body problem, which can in principle be computed to an arbitrary level of precision. So while there's no closed-form solution (as the wikipedia article notes), there is a solution. However, my understanding is that this series solution converges slowly enough as to not be useful in practice.
Ah, that is interesting. I figure Numerical ODE solvers might be faster. But there is philosophical value in a series that is proven to converge for any time t. Do you happen to recall whether it is uniform convergence?
It says that the series should converge for all t, except for systems which begin with zero angular momentum.
It additionally states that:
> in 1930, David Beloriszky calculated that if Sundman’s series were to be used for astronomical observations, then the computations would involve at least 10^8000000 terms
