Atlas3,312 of 3,942

Choreography NC.117

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

Choreography NC.117 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 196.79 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 81585), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000474 of each other at a top speed of 46, line up 192 times a period, and the computed loop closes to 4.6×10⁻²³.

Measured over one period

Period: 196.7939806
Masses: 1 : 1 : 1
Energy: -1.30827
Angular momentum: 0
Closest approach: 4.7×10⁻⁴
Top speed: 46.00
Path length: 477.58
Alignments per period: 192
Topology: 0 (free-group class)
Stability: unstable (|λ|max 8.2×10⁵, published)
Loop closure: 4.6×10⁻²³

Neighbours on the map

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