[noiseman]

I’m not a physicist, so be gentle on me, but it seems that even though you might not know the “initial conditions”, you would certainly know every parameter (mass of each body, relative accelerations and velocities, etc.) at any subsequent snapshot in time. Why couldn’t their motion be predicted from that set of knowns?

[Red Badger]

Because every variable changes with the relationship/distance to the other variables that are themselves also changing relationships..................

[who_would_fardels_bear]

What they are doing is taking the conditions at some starting point then iterating second by second (or some other time interval) and recalculating the three body positions and velocities at each new interval. This is not what is usually meant by solving the problem.

All they're adding is a probability of a long term outcome. This might be useful in determining the likelihood of binary star systems with large planets remaining stable over time or similar questions.

[TexasGator]

There is no closed-form mathematical solution to the problem.

A solution was found using a power series but you would need to use 10^8000000 terms.

Numerical techniques can be used but those are approximations. Those approximations lead errors calculating initial conditions for the next iteration leading to widely divergent solutions.