This five-body gravitational choreography arranges four masses at the corners of a square while a fifth body orchestrates the overall dynamics, with each corner mass tracing its own elliptical sub-orbit. The result combines the rigidity of a square with the flowing motion of individual Keplerian loops at each vertex. Under Newtonian gravity every mass tugs on every other simultaneously, yet the carefully chosen initial positions and velocities keep the configuration repeating periodically rather than dissolving into chaos. In three dimensions the square can tilt and rotate as the system evolves, adding depth to an already intricate dance. Such choreographies illustrate how symmetry and fine-tuned initial conditions can tame the notorious n-body problem.

Four Corners

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