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Choreography SC.189

From Simó (2001)

Choreography SC.189 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.071 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 11571), so a small nudge makes it unravel over a few periods. The bodies pass within 0.074 of each other at a top speed of 3.62, line up 60 times a period, and the computed loop closes to 1.1×10⁻²⁷.

Measured over one period

Period: 14.07096204
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0887
Closest approach: 0.07400
Top speed: 3.616
Path length: 68.578
Alignments per period: 60
Topology: (aaabAbAbABBB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.2×10¹⁷)
Loop closure: 1.1×10⁻²⁷

Neighbours on the map

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