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Choreography SC.120

From Simó (2001)

Choreography SC.120 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.502 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 86143), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0592 of each other at a top speed of 4.49, line up 54 times a period, and the computed loop closes to 1.2×10⁻²⁶.

Measured over one period

Period: 12.50194972
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0903
Closest approach: 0.05925
Top speed: 4.490
Path length: 60.668
Alignments per period: 54
Topology: aaaaaabAbAbAbAbAbABBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 8.6×10¹⁷)
Loop closure: 1.2×10⁻²⁶

Neighbours on the map

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