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Choreography SC.26

From Simó (2001)

Choreography SC.26 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.5246 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 12318), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0257 of each other at a top speed of 6.78, line up 30 times a period, and the computed loop closes to 2.8×10⁻²⁷.

Measured over one period

Period: 6.524606626
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0813
Closest approach: 0.02571
Top speed: 6.779
Path length: 29.780
Alignments per period: 30
Stability: unstable (|λ|max 1.2×10⁷)
Loop closure: 2.8×10⁻²⁷

Neighbours on the map

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