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Hi John-
The problem is incompletely stated. "Three particles interact
only gravitationally' does not exclude the presence of a fourth, or fifth,
or zillionth particle.
Regards,
Jack
On Wed, 2 Jan 2008, John Mallinckrodt wrote:
Apropos of nothing in particular, here's a fun problem whose solution
may raise more questions in your mind:
Three particles interact only gravitationally, follow circular
orbits, and remain at all times collinear. The radii of two of the
orbits is unity. What is the radius of the third?
John Mallinckrodt
Cal Poly Pomona