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Choreography SC.151

From Simó (2001)

Choreography SC.151 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.137 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 75964), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0486 of each other at a top speed of 5.13, line up 60 times a period, and the computed loop closes to 9.0×10⁻²⁹.

Measured over one period

Period: 13.13734134
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1150
Closest approach: 0.04864
Top speed: 5.133
Path length: 62.604
Alignments per period: 60
Stability: unstable (|λ|max 7.6×10¹⁴)
Loop closure: 9.0×10⁻²⁹

Neighbours on the map

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