Atlas3,247 of 3,942

Choreography NC.47

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

Choreography NC.47 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 136.64 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 2428388874), so a small nudge makes it unravel over a few periods. The bodies pass within 0.02 of each other at a top speed of 7.29, line up 90 times a period, and the computed loop closes to 6.5×10⁻²³.

Measured over one period

Period: 136.6443710
Masses: 1 : 1 : 1
Energy: -1.00566
Angular momentum: 0
Closest approach: 0.01997
Top speed: 7.288
Path length: 281.17
Alignments per period: 90
Topology: aaBAbaBAbaBabABabABabAbaBAbaBAbbABabABabABAbaBAbaBABabABabAB (free-group class)
Stability: unstable (|λ|max 2.4×10⁹, published)
Loop closure: 6.5×10⁻²³

Neighbours on the map

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