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Choreography SC.252

From Simó (2001)

Choreography SC.252 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 15.504 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 2.3741e+29), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0367 of each other at a top speed of 5.19, line up 84 times a period, and the computed loop closes to 6.1×10⁻⁶.

Measured over one period

Period: 15.50413312
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99745
Closest approach: 0.03669
Top speed: 5.188
Path length: 72.395
Alignments per period: 84
Stability: unstable (|λ|max 2.4×10²⁹)
Loop closure: 6.1×10⁻⁶

Neighbours on the map

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