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Choreography SC.144

From Simó (2001)

Choreography SC.144 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.936 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 5313), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0625 of each other at a top speed of 4.71, line up 84 times a period, and the computed loop closes to 1.6×10⁻²⁷.

Measured over one period

Period: 12.93604439
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.86032
Closest approach: 0.06254
Top speed: 4.714
Path length: 59.657
Alignments per period: 84
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 5.3×10¹⁶)
Loop closure: 1.6×10⁻²⁷

Neighbours on the map

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