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Choreography SC.164

From Simó (2001)

Choreography SC.164 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.804 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 6.2093e+21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.037 of each other at a top speed of 5.59, line up 66 times a period, and the computed loop closes to 7.5×10⁻²⁵.

Measured over one period

Period: 13.80425981
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0665
Closest approach: 0.03702
Top speed: 5.591
Path length: 62.936
Alignments per period: 66
Stability: unstable (|λ|max 6.2×10²¹)
Loop closure: 7.5×10⁻²⁵

Neighbours on the map

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