Atlas3,611 of 3,915

Choreography SC.59

From Simó (2001)

Choreography SC.59 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.9376 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 11653), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0611 of each other at a top speed of 4.47, line up 30 times a period, and the computed loop closes to 2.9×10⁻²⁹.

Measured over one period

Period: 8.937606577
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0539
Closest approach: 0.06109
Top speed: 4.469
Path length: 42.834
Alignments per period: 30
Stability: unstable (|λ|max 1.2×10¹³)
Loop closure: 2.9×10⁻²⁹

Neighbours on the map

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