I have a partial answer for that. ;-) For at least some functions, iterative solutions exist which converge to correct solutions. For at least some iterative so

I have a partial answer for that. ;-) For at least some functions, iterative solutions exist which converge to correct solutions. For at least some iterative solutions the rate of convergence (the estimated error bounds) is a continuous function: it can be seen that convergence proceeds normally (I should be more careful with that word) as long as the estimated error bounds for the iteration is larger than the computationally induced error. I'll hazard a guess that with constraints some formulations which model a three body problem are solvable to the point where the estimated error bounds approaches the computationally induced error due to floating point imprecision. The thing about the three body problem, same as here, is that there are regions in the initial position and velocity space where very small changes produce extremely large differences in function output. There has been some work / recognition of the value of topological understanding to orbital mechanics, although I can't find whatever I read a few months ago. Best I could find was https://en.wikipedia.org/wiki/Symplectic_geometry https://en.wikipedia.org/wiki/Symplectic_geometry and this DDG search looks promising: https://duckduckgo.com/?q=symplectic+integrators+solar+system&t=ffab&ia=web https://duckduckgo.com/?q=symplectic+integrators+solar+syste...