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Choreography SC.137

From Simó (2001)

Choreography SC.137 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.75 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 42475), so a small nudge makes it unravel over a few periods. The bodies pass within 0.031 of each other at a top speed of 6.2, line up 66 times a period, and the computed loop closes to 2.9×10⁻²⁷.

Measured over one period

Period: 12.74968814
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1040
Closest approach: 0.03097
Top speed: 6.197
Path length: 57.820
Alignments per period: 66
Stability: unstable (|λ|max 4.2×10¹⁰)
Loop closure: 2.9×10⁻²⁷

Neighbours on the map

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