Why can't a three/more body problem be reduced to a one-body problem?

AI Thread Summary
The discussion centers on the complexity of the three-body problem compared to the two-body problem, highlighting that while the two-body problem can be simplified using an equivalent one-body approach with reduced mass, this method fails for three or more bodies. Participants note that finding a suitable coordinate transformation is challenging, as relative coordinates require three dimensions to fully specify the system, which does not simplify the problem. The conversation emphasizes that for three bodies, the independent vectors can be reduced to two, along with the center of mass coordinate, but this still does not lead to a straightforward solution. Overall, the intricacies of multi-body dynamics make reduction to a one-body problem unfeasible. The complexities of the three-body problem remain a significant challenge in physics.
neelakash
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We know a two body problem may be analysed as an equivalent one body problem.Why a three/more body problem cannot be reduced to a one-body problem?

I think in that case we do not find an equivalent reduced mass...
Anyone can say something?
 
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Try to come up with a coordinate transformation that does any good. Relative coordinates don't work, you need three to specify everything. This is no better than the starting position. Just give it a shot and you'll see.
 
For three bodies, you can reduce the independent vectors to two plus the coordinate of the overall center of mass.
 
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