There’s a difference between solving it (providing a precise mathematical formula) and estimating the positions of these three bodies for a certain time frame.
What people used to do in the past was the latter – based on observation, they were able to predict the movement of celestial bodies without knowing the exact rules their movements are based on.
And, to a certain extent, that’s what we’re still doing nowadays to “solve” the n-body problem. We have models that aren’t 100% accurate. The further you go in time, the less precise they are.
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