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Choreography SC.159

From Simó (2001)

Choreography SC.159 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.749 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 78475), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0164 of each other at a top speed of 8.27, line up 54 times a period, and the computed loop closes to 4.0×10⁻²⁷.

Measured over one period

Period: 13.74936953
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0104
Closest approach: 0.01640
Top speed: 8.273
Path length: 63.667
Alignments per period: 54
Stability: unstable (|λ|max 7.8×10¹⁵)
Loop closure: 4.0×10⁻²⁷

Neighbours on the map

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