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Choreography SC.64

From Simó (2001)

Choreography SC.64 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.3258 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 1.4232000000000002e+25), so a small nudge makes it unravel over a few periods. The bodies pass within 0.172 of each other at a top speed of 2.87, line up 36 times a period, and the computed loop closes to 5.6×10⁻²⁶.

Measured over one period

Period: 9.325796801
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1003
Closest approach: 0.1718
Top speed: 2.872
Path length: 45.027
Alignments per period: 36
Topology: (abAB)² (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.4×10²⁵)
Loop closure: 5.6×10⁻²⁶

Neighbours on the map

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