Atlas3,537 of 3,942

Choreography SC.153

From Simó (2001)

Choreography SC.153 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 13.467 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 2.6809999999999997e+26), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0491 of each other at a top speed of 4.45, line up 42 times a period, and the computed loop closes to 9.2×10⁻²⁵.

Measured over one period

Period: 13.46710167
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0533
Closest approach: 0.04914
Top speed: 4.454
Path length: 66.176
Alignments per period: 42
Topology: aaaabAbAbAbABBBB (free-group class, read from the drawing)
Stability: unstable (|λ|max 2.7×10²⁶)
Loop closure: 9.2×10⁻²⁵

Neighbours on the map

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