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Choreography SC.29

From Simó (2001)

Choreography SC.29 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.5769 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 66162), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0553 of each other at a top speed of 4.64, line up 24 times a period, and the computed loop closes to 2.2×10⁻²⁹.

Measured over one period

Period: 6.576872526
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0674
Closest approach: 0.05529
Top speed: 4.642
Path length: 31.179
Alignments per period: 24
Topology: aaaabAbAbAbABBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 6.6×10⁷)
Loop closure: 2.2×10⁻²⁹

Neighbours on the map

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