Four equal masses chase one another around a shared circular path in this four-body gravitational choreography. Unlike most n-body systems, which eventually drift into chaos or collision, this configuration is a known periodic solution: the bodies return to their starting arrangement again and again, tracing overlapping elliptical loops that together outline a circle. The setup belongs to the family of n-body choreographies discovered by mathematicians and celestial mechanicians studying the three- and four-body problems. In three dimensions the motion is symmetric — each mass follows the same shaped orbit, offset by a quarter period from its neighbors.

Dancing in a Circle

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