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Choreography SC.182

From Simó (2001)

Choreography SC.182 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.977 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 61065), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0942 of each other at a top speed of 3.78, line up 48 times a period, and the computed loop closes to 1.2×10⁻²⁶.

Measured over one period

Period: 13.97726589
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0105
Closest approach: 0.09418
Top speed: 3.778
Path length: 68.173
Alignments per period: 48
Stability: unstable (|λ|max 6.1×10¹⁷)
Loop closure: 1.2×10⁻²⁶

Neighbours on the map

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