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Choreography SC.103

From Simó (2001)

Choreography SC.103 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.558 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 25249), so a small nudge makes it unravel over a few periods. The bodies pass within 0.075 of each other at a top speed of 4.34, line up 48 times a period, and the computed loop closes to 4.6×10⁻²⁹.

Measured over one period

Period: 11.55773348
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0562
Closest approach: 0.07501
Top speed: 4.339
Path length: 55.557
Alignments per period: 48
Topology: aaaaaaaabAbAbAbAbAbAbAbABBBBBBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.5×10⁹)
Loop closure: 4.6×10⁻²⁹

Neighbours on the map

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