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Choreography SC.34

From Simó (2001)

Choreography SC.34 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.7734 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 81869), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00252 of each other at a top speed of 20.9, line up 24 times a period, and the computed loop closes to 5.4×10⁻²⁷.

Measured over one period

Period: 6.773364752
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.93344
Closest approach: 0.002517
Top speed: 20.85
Path length: 31.370
Alignments per period: 24
Stability: unstable (|λ|max 8.2×10¹⁵)
Loop closure: 5.4×10⁻²⁷

Neighbours on the map

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