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Choreography SC.167

From Simó (2001)

Choreography SC.167 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.914 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 6.239100000000001e+25), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00621 of each other at a top speed of 13.7, line up 60 times a period, and the computed loop closes to 9.0×10⁻²⁶.

Measured over one period

Period: 13.91350082
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.91903
Closest approach: 0.006207
Top speed: 13.65
Path length: 63.178
Alignments per period: 60
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 6.2×10²⁵)
Loop closure: 9.0×10⁻²⁶

Neighbours on the map

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