Atlas3,320 of 3,915

Choreography NC.51

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

Choreography NC.51 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 57.287 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 11835511238254), 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 8.22, line up 108 times a period, and the computed loop closes to 8.9×10⁻²⁰.

Measured over one period

Period: 57.28713793
Masses: 1 : 1 : 1
Energy: -1.92926
Angular momentum: 0
Closest approach: 0.01621
Top speed: 8.217
Path length: 161.53
Alignments per period: 108
Stability: unstable (|λ|max 1.2×10¹³, published)
Loop closure: 8.9×10⁻²⁰

Neighbours on the map

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