anand@utastro.UUCP (Anand Sivaramakrishnan) (09/30/85)
Some answers to some questions... < 1. Why is the three- or many-bodied problem unsolvable? We cannot find enough independent functions that are 'constants of motion' (eg. components of momentum, angular momentum, energy etc). That's why the more-than-two body problem is 'insoluble' (not integrable). < 2. Do the three-body problems apply for systems where the mass of < one of the bodies is vanishingly small compared to the others < (such as in a Voyager/Jupiter/Sun system)? Yes, indeed.... the motion of the third, light body is not integrable. By the way (looky here, Ethan!), the solution of such problems as perturbation problems is only valid for some of the possible orbits of the third (light) body. There are many cases where these perturbation theories break down very rapidly (a few orbits, even). Perturbation theories are usually good for the periodic sorts of orbits one finds in the solar system. < 4. Is the solution to all this merely one of computational < fortitude? No. JPL has made the approximations less approximate, as the original poster guessed. < AN ensuing discussion might be of value, unless the answer is really < very simple and obvious, which it does not seem to be. < Dick Pierce