Atlas3,283 of 3,915

Choreography NC.59

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

Choreography NC.59 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 64.23 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 18851011617285), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0162 of each other at a top speed of 7.92, line up 108 times a period, and the computed loop closes to 1.2×10⁻¹⁷.

Measured over one period

Period: 64.23008621
Masses: 1 : 1 : 1
Energy: -1.87825
Angular momentum: 0
Closest approach: 0.01622
Top speed: 7.917
Path length: 184.38
Alignments per period: 108
Stability: unstable (|λ|max 1.9×10¹³, 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.