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Choreography SC.127

From Simó (2001)

Choreography SC.127 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.616 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 1.1351e+23), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0051 of each other at a top speed of 14.8, line up 36 times a period, and the computed loop closes to 6.4×10⁻²⁴.

Measured over one period

Period: 12.61560314
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.97486
Closest approach: 0.005096
Top speed: 14.75
Path length: 60.334
Alignments per period: 36
Stability: unstable (|λ|max 1.1×10²³)
Loop closure: 6.4×10⁻²⁴

Neighbours on the map

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