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Choreography SC.70

From Simó (2001)

Choreography SC.70 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.8624 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 4.6519e+22), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00547 of each other at a top speed of 13.9, line up 42 times a period, and the computed loop closes to 5.3×10⁻⁷.

Measured over one period

Period: 9.862427413
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.94573
Closest approach: 0.005468
Top speed: 13.93
Path length: 45.846
Alignments per period: 42
Stability: unstable (|λ|max 4.7×10²²)
Loop closure: 5.3×10⁻⁷

Neighbours on the map

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