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Choreography SC.140

From Simó (2001)

Choreography SC.140 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.793 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 2.3036e+31), so a small nudge makes it unravel over a few periods. The bodies pass within 0.139 of each other at a top speed of 3.1, line up 36 times a period, and the computed loop closes to 3.4×10⁻⁹.

Measured over one period

Period: 12.79337087
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0481
Closest approach: 0.1388
Top speed: 3.096
Path length: 63.421
Alignments per period: 36
Stability: unstable (|λ|max 2.3×10³¹)
Loop closure: 3.4×10⁻⁹

Neighbours on the map

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