Atlas3,348 of 3,915

Choreography NC.55

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

Choreography NC.55 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 231.63 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 15424345), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00398 of each other at a top speed of 16.2, line up 108 times a period, and the computed loop closes to 5.9×10⁻²³.

Measured over one period

Period: 231.6336755
Masses: 1 : 1 : 1
Energy: -0.781469
Angular momentum: 0
Closest approach: 0.003984
Top speed: 16.18
Path length: 396.34
Alignments per period: 108
Stability: unstable (|λ|max 1.5×10⁸, published)
Loop closure: 5.9×10⁻²³

Neighbours on the map

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