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Choreography SC.9

From Simó (2001)

Choreography SC.9 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.1441 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 14581), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0266 of each other at a top speed of 6.75, line up 12 times a period, and the computed loop closes to 3.7×10⁻²⁹.

Measured over one period

Period: 5.144085707
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.98835
Closest approach: 0.02662
Top speed: 6.750
Path length: 24.604
Alignments per period: 12
Stability: unstable (|λ|max 1.5×10¹¹)
Loop closure: 3.7×10⁻²⁹

Neighbours on the map

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