Atlas3,333 of 3,942

Choreography NC.54

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

Choreography NC.54 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 233.81 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 5685819), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0389 of each other at a top speed of 5.24, line up 102 times a period, and the computed loop closes to 2.5×10⁻²⁴.

Measured over one period

Period: 233.8131198
Masses: 1 : 1 : 1
Energy: -0.758091
Angular momentum: 0
Closest approach: 0.03893
Top speed: 5.243
Path length: 417.50
Alignments per period: 102
Topology: aaBAbaBAbABabaBAbaBABabAbaBAbaBBabAAbaBAbaBabABAbaBAbabABaBAbaBAbbAB (free-group class)
Stability: unstable (|λ|max 5.7×10⁶, published)
Loop closure: 2.5×10⁻²⁴

Neighbours on the map

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