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Choreography SC.110

From Simó (2001)

Choreography SC.110 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 11.849 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 43383), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0525 of each other at a top speed of 4.92, line up 42 times a period, and the computed loop closes to 8.5×10⁻²⁷.

Measured over one period

Period: 11.84890528
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0490
Closest approach: 0.05253
Top speed: 4.919
Path length: 55.775
Alignments per period: 42
Stability: unstable (|λ|max 4.3×10¹⁷)
Loop closure: 8.5×10⁻²⁷

Neighbours on the map

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