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Choreography SC.78

From Simó (2001)

Choreography SC.78 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.257 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 59909), so a small nudge makes it unravel over a few periods. The bodies pass within 0.076 of each other at a top speed of 4.11, line up 36 times a period, and the computed loop closes to 1.8×10⁻²⁷.

Measured over one period

Period: 10.25675575
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 0.99033
Closest approach: 0.07604
Top speed: 4.112
Path length: 49.289
Alignments per period: 36
Stability: unstable (|λ|max 6.0×10¹³)
Loop closure: 1.8×10⁻²⁷

Neighbours on the map

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