Atlas3,286 of 3,942

Choreography NC.144

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

Choreography NC.144 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 177.57 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 22206692403), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000124 of each other at a top speed of 90, line up 246 times a period, and the computed loop closes to 3.0×10⁻¹⁶.

Measured over one period

Period: 177.5680030
Masses: 1 : 1 : 1
Energy: -1.64682
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 89.95
Path length: 483.16
Alignments per period: 246
Topology: 0 (free-group class)
Stability: unstable (|λ|max 2.2×10¹⁰, published)
Loop closure: 3.0×10⁻¹⁶

Neighbours on the map

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