Agreed. A many-body problem has no analytic solution - it requires zillions of calcs to find a best solution.
But by 2029, your wristwatch will be able to do those calcs.
> But by 2029, your wristwatch will be able to do those calcs.
Wristwatch? No, those will no longer exist. The brain-chip will simply display a heads-up display directly onto your retina (giving you the time in all time zones, along with your exact location), do your taxes, calculate orbital trajectories two millenia out, and project the fourteen most-likely-successful pick-up lines to the four-breasted genetically modified hottie in the corner.
Of course, if there's a "President Hillary" between now and then, that chip will *broadcast* your position, will modify your behavior, make you feel happy whenever Madame President appears (which will be every ten minutes) and will be mandatory.
Only if it has accurate enough data. The accuracy of the existing orbital elements is instrument, not numerically, limited.