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Choreography SC.195

From Simó (2001)

Choreography SC.195 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 14.186 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 21602), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0627 of each other at a top speed of 4.35, line up 114 times a period, and the computed loop closes to 2.5×10⁻²⁸.

Measured over one period

Period: 14.18557637
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0236
Closest approach: 0.06268
Top speed: 4.346
Path length: 64.592
Alignments per period: 114
Stability: unstable (|λ|max 2.2×10⁷)
Loop closure: 2.5×10⁻²⁸

Neighbours on the map

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