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Choreography SC.302

From Simó (2001)

Choreography SC.302 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 16.363 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 26948), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0586 of each other at a top speed of 4.5, line up 138 times a period, and the computed loop closes to 1.4×10⁻²⁸.

Measured over one period

Period: 16.36332847
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0184
Closest approach: 0.05859
Top speed: 4.504
Path length: 73.757
Alignments per period: 138
Stability: unstable (|λ|max 2.7×10⁷)
Loop closure: 1.4×10⁻²⁸

Neighbours on the map

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