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Choreography SC.33

From Simó (2001)

Choreography SC.33 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.7606 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 15787), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00148 of each other at a top speed of 26.9, line up 18 times a period, and the computed loop closes to 3.0×10⁻²⁵.

Measured over one period

Period: 6.760617976
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.91769
Closest approach: 0.001478
Top speed: 26.93
Path length: 31.452
Alignments per period: 18
Stability: unstable (|λ|max 1.6×10¹⁷)
Loop closure: 3.0×10⁻²⁵

Neighbours on the map

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