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Choreography SC.4

From Simó (2001)

Choreography SC.4 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 3.7719 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 13181), so a small nudge makes it unravel over a few periods. The bodies pass within 0.108 of each other at a top speed of 3.01, line up 18 times a period, and the computed loop closes to 5.2×10⁻³⁰.

Measured over one period

Period: 3.771948782
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1219
Closest approach: 0.1082
Top speed: 3.010
Path length: 18.277
Alignments per period: 18
Stability: unstable (|λ|max 1.3×10⁶)
Loop closure: 5.2×10⁻³⁰

Neighbours on the map

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