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Choreography SC.244

From Simó (2001)

Choreography SC.244 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.329 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 79769), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0305 of each other at a top speed of 6.33, line up 66 times a period, and the computed loop closes to 5.4×10⁻²⁸.

Measured over one period

Period: 15.32894687
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0964
Closest approach: 0.03053
Top speed: 6.329
Path length: 71.316
Alignments per period: 66
Stability: unstable (|λ|max 8.0×10¹⁷)
Loop closure: 5.4×10⁻²⁸

Neighbours on the map

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