Atlas3,581 of 3,915

Choreography SC.138

From Simó (2001)

Choreography SC.138 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.756 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 1.177e+23), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0606 of each other at a top speed of 4.51, line up 48 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 12.75647195
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0762
Closest approach: 0.06060
Top speed: 4.507
Path length: 61.814
Alignments per period: 48
Stability: unstable (|λ|max 1.2×10²³)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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