I don't have more than a cursory knowledge of the solution, but the Three-body problem wikipedia page should have enough info to get you set in the right direction: https://en.wikipedia.org/wiki/Three-body_problem#Sundman's_t...

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