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Choreography SC.128

From Simó (2001)

Choreography SC.128 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.623 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 29935), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0639 of each other at a top speed of 4.2, line up 66 times a period, and the computed loop closes to 1.7×10⁻²⁵.

Measured over one period

Period: 12.62305351
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0705
Closest approach: 0.06390
Top speed: 4.196
Path length: 59.027
Alignments per period: 66
Topology: aaaaaabAbAbAbAbAbABBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 3.0×10²⁰)
Loop closure: 1.7×10⁻²⁵

Neighbours on the map

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