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Choreography SC.25

From Simó (2001)

Choreography SC.25 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.5237 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 15919), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0554 of each other at a top speed of 4.72, line up 30 times a period, and the computed loop closes to 3.4×10⁻²⁸.

Measured over one period

Period: 6.523672047
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1162
Closest approach: 0.05545
Top speed: 4.721
Path length: 30.971
Alignments per period: 30
Topology: aaaabAbAbAbABBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 1.6×10¹¹)
Loop closure: 3.4×10⁻²⁸

Neighbours on the map

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