Atlas3,222 of 3,942

Choreography NC.125

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024)

Choreography NC.125 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 287.91 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024). Choreographies whose knot is not a power of the figure-eight’s: three bodies on one closed curve with a topology of its own. Computed to 180 digits; all unstable. It is unstable (largest Floquet multiplier 9257692), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0664 of each other at a top speed of 3.98, line up 216 times a period, and the computed loop closes to 3.8×10⁻²⁵.

Measured over one period

Period: 287.9088261
Masses: 1 : 1 : 1
Energy: -1.09860
Angular momentum: 0
Closest approach: 0.06641
Top speed: 3.981
Path length: 657.73
Alignments per period: 216
Topology: aaBAbaBAbaBAbaBAbaBabABabABabABabABabABabABabABabAbaBAbaBAbaBAbaBAbbABabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 9.3×10⁶, published)
Loop closure: 3.8×10⁻²⁵

Neighbours on the map

All Nontrivial choreographies, the families of periodic three-body orbits, or the atlas map.