Atlas3,300 of 3,915

Choreography NC.42

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

Choreography NC.42 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 170.49 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 57260816701675), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0336 of each other at a top speed of 5.75, line up 96 times a period, and the computed loop closes to 1.2×10⁻¹⁷.

Measured over one period

Period: 170.4906541
Masses: 1 : 1 : 1
Energy: -0.854938
Angular momentum: 0
Closest approach: 0.03363
Top speed: 5.749
Path length: 306.62
Alignments per period: 96
Stability: unstable (|λ|max 5.7×10¹³, published)
Loop closure: 1.2×10⁻¹⁷

Neighbours on the map

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