It is possible to write an n-body simulation program that only halts its step-by-step iteration if one body collides with another (specific) body or reaches a specific location.

Now, is it possible to tell analytically, without running the program, if it halts (at an arbitrary point in the future, or within a certain number of steps)? If so, the n-body/trajectory finding problem is solved, efficiently.

But (n>=3) n-body systems have been shown to be chaotic, depending sensitively on the initial state of the system, so this doesn't seem to be generally possible without brute force computation.

So what about this chaos/mathematical-logical-temporal relation/equations between state variables (body positions and velocities) make this halting problem (effectively/efficiently) unsolvable, and how does it relate to other computational systems where the halting problem applies, like turing machines?

Edit: https://cs.stackexchange.com/questions/43181/is-the-unsolvab...