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Choreography SC.155

From Simó (2001)

Choreography SC.155 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.67 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 69167), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0168 of each other at a top speed of 8.59, line up 54 times a period, and the computed loop closes to 5.1×10⁻²⁷.

Measured over one period

Period: 13.66972169
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.98386
Closest approach: 0.01679
Top speed: 8.593
Path length: 62.885
Alignments per period: 54
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 6.9×10¹⁷)
Loop closure: 5.1×10⁻²⁷

Neighbours on the map

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