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**N-Body Problem -- ideas?**

First of all I would like some explanation on why one can't find a GENERAL solution for the N-body problem, and what exactly we have to use in its place.

Secondly, I want to know if anybody understands these vague ideas of mine and how they would work...

Let's say, for each particle in the system, we could imagine a "virtual particle" (which has nothing to do with the virtual particles from other branches of physics, which I know nothing about) whose motion could be traced as a function of the initial positions, velocities, etc. of all of the other particles, and instead of regarding the given particle's motion as a function of all the other particles we could simply follow its motion with respect to the virtual particle, so it would be reduced to a 2-body problem or perhaps not even that, if we assume that the virtual particle's motion is unaffected by the actual particle that is following it. And perhaps we might need to make new rules on virtual particle motion, how they react with each other, do they fall in on each other, etc...

A virtual particle would be somewhat similar to center of mass, I think? Regarding the center of mass itself as a virtual particle, its velocity at any one moment can be regarded as the vector sum of the velocities of all the other particles at that moment (not sure how relativity would play into it).

Sorry if this makes no sense...