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Choreography SC.304

From Simó (2001)

Choreography SC.304 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.422 time units, published by Simó (2001). Carles Simó’s catalogue of three-body choreographies with nonzero angular momentum, the curves that made choreographies famous. All unstable except the figure-eight. It is unstable (largest Floquet multiplier 23154), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0457 of each other at a top speed of 5.34, line up 78 times a period, and the computed loop closes to 2.1×10⁻²⁶.

Measured over one period

Period: 16.42216943
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1066
Closest approach: 0.04575
Top speed: 5.338
Path length: 78.001
Alignments per period: 78
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 2.3×10²⁰)
Loop closure: 2.1×10⁻²⁶

Neighbours on the map

All Simó’s choreographies, the families of periodic three-body orbits, or the atlas map.