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Choreography SC.15

From Simó (2001)

Choreography SC.15 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.5466 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 26756), so a small nudge makes it unravel over a few periods. The bodies pass within 0.13 of each other at a top speed of 3.21, line up 18 times a period, and the computed loop closes to 7.9×10⁻²⁹.

Measured over one period

Period: 5.546618356
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.93457
Closest approach: 0.1304
Top speed: 3.214
Path length: 26.794
Alignments per period: 18
Stability: unstable (|λ|max 2.7×10¹⁷)
Loop closure: 7.9×10⁻²⁹

Neighbours on the map

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