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Choreography SC.3

From Simó (2001)

Choreography SC.3 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 3.6249 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 87455), so a small nudge makes it unravel over a few periods. The bodies pass within 0.136 of each other at a top speed of 3.08, line up 6 times a period, and the computed loop closes to 3.2×10⁻³⁰.

Measured over one period

Period: 3.624872250
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99698
Closest approach: 0.1356
Top speed: 3.077
Path length: 18.270
Alignments per period: 6
Stability: unstable (|λ|max 8.7×10⁶)
Loop closure: 3.2×10⁻³⁰

Neighbours on the map

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