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Choreography SC.101

From Simó (2001)

Choreography SC.101 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.515 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 73747), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0822 of each other at a top speed of 4.01, line up 54 times a period, and the computed loop closes to 4.0×10⁻²⁷.

Measured over one period

Period: 11.51527252
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1159
Closest approach: 0.08215
Top speed: 4.011
Path length: 55.784
Alignments per period: 54
Stability: unstable (|λ|max 7.4×10¹⁶)
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.