Maybe I’ve been asleep, but can computers (from PCs to Super Computers) solve the three body problem? Or, do they simply help us to make more accurate approximations? If computers cannot solve it, is it because our best algorithms are limited by our mortal capabilities? (In other words, is the model we use simply limited by the abilities of those who built the model?) - Jinx
Three-body problems usually have no analytical solutions, i.e. something you can write out as a formula. But it’s possible to calculate a numerical solution (i.e. a table of values instead of a formula) to an arbitrary precision.
Out of curiosity, what’s the Three Body Problem?
In Newtonian (classical) physocs, every body with a mass attracts every other body (with a mass) with a force that depends only on their weights and the distance (F = G m[sub]1[/sub] m[sub]2[/sub] / R[sup]2[/sup]).
If you have two bodies, it’s farily straightforward to calculate these forces, and the effect they will have on the trajectories of the two bodies. (They will most likelly end up in elliptical orbit around their center of gravity.)
For three bodies, however, it gets tricky. It’s still fairly easy to calculate the forces at any given time, but to predict the trajectories gets really hairy. There is no (known) analytical expression to predict the position of the three bodies at an arbitrary future time. It is, of course, possible to calculate numerically with an arbitrary precision, by calculating the forces at time T[sub]1[/sub], use this to predict where they will be at time T[sub]1[/sub]+epsilon, etc.
I believe that the OP wanted to know if there had been any advances along those lines, but as far as I know there haven’t been any. (Does anyone know if it has been proved that there’s no analytical solution to the three-body problem?)
[joke]
In Aristotelian physics, everything was deterministic and well-defined.
In Newtonian physics, we can’t solve the three-body problem.
In Einsteinian physics, we can’t solve the two-body problem.
In Heisenbergian physics, we can’t even know where one particle is.
In Quantum Electrodynamics, we can’t even solve the equation for vacuum.
[/joke]
Further problem: many cases in the Three Body Problem give chaotic solutions - sensitivity to vanishingly small differences in initial conditions - so even higher numerical precision won’t help.