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Choreography SC.200

From Simó (2001)

Choreography SC.200 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.261 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 93118), so a small nudge makes it unravel over a few periods. The bodies pass within 0.14 of each other at a top speed of 3.18, line up 96 times a period, and the computed loop closes to 1.5×10⁻²⁸.

Measured over one period

Period: 14.26068240
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0762
Closest approach: 0.1404
Top speed: 3.179
Path length: 69.416
Alignments per period: 96
Topology: aaaaaaabAbAbAbAbAbAbABBBBBBB (free-group class, read from the drawing, shape period T/2)
Stability: unstable (|λ|max 9.3×10¹¹)
Loop closure: 1.5×10⁻²⁸

Neighbours on the map

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