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Choreography SC.77

From Simó (2001)

Choreography SC.77 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.251 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 53102), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0864 of each other at a top speed of 3.88, line up 42 times a period, and the computed loop closes to 6.5×10⁻²⁷.

Measured over one period

Period: 10.25128512
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0829
Closest approach: 0.08641
Top speed: 3.877
Path length: 49.747
Alignments per period: 42
Stability: unstable (|λ|max 5.3×10¹⁶)
Loop closure: 6.5×10⁻²⁷

Neighbours on the map

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