3-body solution in two dimensions

Loren Booda
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Are there any exact solutions for two-dimensional projections of 3-body problems?
 
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I really don't know anything about 3-body problems so I should probably just keep quiet, but...

If you have an unknown trajectory R(t) = <x(t),y(t),z(t)> it seems to me that if we could exactly solve for the trajectory in each of two planes we could solve the original trajectory exactly. In the z = 0 plane you would have R(t) = <x(t),y(t)> and in the y = 0 plane you would know R(t) = <x(t),z(t)> with perhaps a different parameterization. I would think having those two you could build the 3D version exactly, which, apparently, you can't do.

Disclaimer: The above may be worthless speculation.
 

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