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Choreography SC.255

From Simó (2001)

Choreography SC.255 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.54 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 7.6491e+27), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0458 of each other at a top speed of 5.44, line up 60 times a period, and the computed loop closes to 9.8×10⁻⁷.

Measured over one period

Period: 15.54020989
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0429
Closest approach: 0.04577
Top speed: 5.439
Path length: 74.090
Alignments per period: 60
Topology: (aaaabAbAbAbABBBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 7.6×10²⁷)
Loop closure: 9.8×10⁻⁷

Neighbours on the map

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