Atlas3,270 of 3,942

Choreography NC.63

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

Choreography NC.63 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 89.302 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 4423), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000356 of each other at a top speed of 53, line up 114 times a period, and the computed loop closes to 8.8×10⁻²⁴.

Measured over one period

Period: 89.30238245
Masses: 1 : 1 : 1
Energy: -1.56413
Angular momentum: 0
Closest approach: 3.6×10⁻⁴
Top speed: 53.01
Path length: 237.02
Alignments per period: 114
Topology: aaBAbaBAbaBAbaBabABabABabABAbaBAbaBAbaBABabABabABabAbaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: unstable (|λ|max 4423, published)
Loop closure: 8.8×10⁻²⁴

Neighbours on the map

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