Atlas3,225 of 3,942

Choreography NC.84

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

Choreography NC.84 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 233.66 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 21701367), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00599 of each other at a top speed of 13, line up 150 times a period, and the computed loop closes to 5.2×10⁻²³.

Measured over one period

Period: 233.6592029
Masses: 1 : 1 : 1
Energy: -0.988929
Angular momentum: 0
Closest approach: 0.005990
Top speed: 12.99
Path length: 475.51
Alignments per period: 150
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABAbaBAbaBAbaBAbaBAbaBAbaBABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbbABabAB (free-group class)
Stability: unstable (|λ|max 2.2×10⁷, published)
Loop closure: 5.2×10⁻²³

Neighbours on the map

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