Atlas3,579 of 3,915

Choreography SC.133

From Simó (2001)

Choreography SC.133 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 12.652 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 26028), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0919 of each other at a top speed of 3.69, line up 42 times a period, and the computed loop closes to 2.1×10⁻²⁷.

Measured over one period

Period: 12.65201983
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0889
Closest approach: 0.09190
Top speed: 3.688
Path length: 62.189
Alignments per period: 42
Stability: unstable (|λ|max 2.6×10¹⁵)
Loop closure: 2.1×10⁻²⁷

Neighbours on the map

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