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Choreography SC.88

From Simó (2001)

Choreography SC.88 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.685 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 5.2674e+21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0464 of each other at a top speed of 5.08, line up 48 times a period, and the computed loop closes to 5.8×10⁻²⁶.

Measured over one period

Period: 10.68537056
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0960
Closest approach: 0.04641
Top speed: 5.078
Path length: 50.205
Alignments per period: 48
Stability: unstable (|λ|max 5.3×10²¹)
Loop closure: 5.8×10⁻²⁶

Neighbours on the map

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