So the computer based solution proposed by Newton and Turing is rejected because the system is chaotic, meaning a general solution will always diverge from reality.
What I don’t get is: this should still be good enough Run your solution every month or so, with updated measurements, and you’ll have an ongoing “forecast” of conditions.
I’m referencing weather because that’s we do. A weather forecast is a prediction of a chaotic system, but of one which changes every day or so. Prediction difficulty is dependent on local conditions and weather type, but we can still make predictions.
A gravitational system of 4 mutually interacting bodies is muuuuuch simpler than weather, and could be predicted far enough in advance to let a civilization adapt and persist!
More a nitpick for the overall series, but if I were a swordweilder I’d just start terraforming Mars or Venus and constantly be saying, “Hey, what a lovely planet we’re making. It could look like anything, be home to anyone. I sure do wonder if our interstellar neighbors would like to have it in exchange for us maintaining some autonomy? Maybe a mutual partnership? A jointly operated particle accelerator?”