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Choreography SC.66

From Simó (2001)

Choreography SC.66 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.4239 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 29855), so a small nudge makes it unravel over a few periods. The bodies pass within 0.161 of each other at a top speed of 2.91, line up 48 times a period, and the computed loop closes to 6.0×10⁻³⁰.

Measured over one period

Period: 9.423947190
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1035
Closest approach: 0.1612
Top speed: 2.912
Path length: 46.400
Alignments per period: 48
Stability: unstable (|λ|max 3.0×10⁸)
Loop closure: 6.0×10⁻³⁰

Neighbours on the map

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