Atlas3,677 of 3,915

Choreography SC.62

From Simó (2001)

Choreography SC.62 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 9.0553 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 23121), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0666 of each other at a top speed of 4.32, line up 36 times a period, and the computed loop closes to 3.2×10⁻²⁹.

Measured over one period

Period: 9.055345313
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.1198
Closest approach: 0.06663
Top speed: 4.322
Path length: 43.699
Alignments per period: 36
Stability: unstable (|λ|max 2.3×10¹³)
Loop closure: 3.2×10⁻²⁹

Neighbours on the map

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