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Choreography SC.38

From Simó (2001)

Choreography SC.38 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.8615 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 8522700000000002), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0703 of each other at a top speed of 4.06, line up 18 times a period, and the computed loop closes to 1.8×10⁻²⁷.

Measured over one period

Period: 6.861510504
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1052
Closest approach: 0.07031
Top speed: 4.060
Path length: 31.447
Alignments per period: 18
Topology: (abAB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 8.5×10¹⁵)
Loop closure: 1.8×10⁻²⁷

Neighbours on the map

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