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Choreography SC.342

From Simó (2001)

Choreography SC.342 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 17.251 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 46248), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0387 of each other at a top speed of 5.55, line up 102 times a period, and the computed loop closes to 7.5×10⁻²⁷.

Measured over one period

Period: 17.25061063
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1173
Closest approach: 0.03875
Top speed: 5.553
Path length: 79.822
Alignments per period: 102
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 4.6×10¹⁵)
Loop closure: 7.5×10⁻²⁷

Neighbours on the map

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