Atlas3,303 of 3,915

Choreography NC.60

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

Choreography NC.60 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 197.39 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 33401703741), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0447 of each other at a top speed of 5, line up 114 times a period, and the computed loop closes to 2.0×10⁻²⁰.

Measured over one period

Period: 197.3863645
Masses: 1 : 1 : 1
Energy: -0.897540
Angular momentum: 0
Closest approach: 0.04470
Top speed: 5.001
Path length: 382.19
Alignments per period: 114
Stability: unstable (|λ|max 3.3×10¹⁰, published)
Loop closure: 2.0×10⁻²⁰

Neighbours on the map

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