Atlas3,321 of 3,942

Choreography NC.24

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

Choreography NC.24 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 184.32 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 1265874396821), so a small nudge makes it unravel over a few periods. The bodies pass within 0.105 of each other at a top speed of 3.35, line up 84 times a period, and the computed loop closes to 3.2×10⁻¹⁹.

Measured over one period

Period: 184.3245497
Masses: 1 : 1 : 1
Energy: -0.681858
Angular momentum: 0
Closest approach: 0.1048
Top speed: 3.349
Path length: 282.16
Alignments per period: 84
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.3×10¹², published)
Loop closure: 3.2×10⁻¹⁹

Neighbours on the map

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