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Choreography SC.49

From Simó (2001)

Choreography SC.49 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.1482 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 12459), so a small nudge makes it unravel over a few periods. The bodies pass within 0.172 of each other at a top speed of 2.79, line up 36 times a period, and the computed loop closes to 3.2×10⁻³⁰.

Measured over one period

Period: 8.148218012
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1112
Closest approach: 0.1724
Top speed: 2.793
Path length: 40.206
Alignments per period: 36
Topology: aabAbABB (free-group class, read from the drawing, shape period T/2)
Stability: unstable (|λ|max 1.2×10⁶)
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.