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Choreography SC.178

From Simó (2001)

Choreography SC.178 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.97 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 98652), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0246 of each other at a top speed of 6.97, line up 72 times a period, and the computed loop closes to 7.2×10⁻²⁵.

Measured over one period

Period: 13.96963674
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0565
Closest approach: 0.02458
Top speed: 6.968
Path length: 63.428
Alignments per period: 72
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 9.9×10¹⁴)
Loop closure: 7.2×10⁻²⁵

Neighbours on the map

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