Atlas3,236 of 3,915

Choreography NC.138

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

Choreography NC.138 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 236.88 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 10990407735), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0027 of each other at a top speed of 19.3, line up 240 times a period, and the computed loop closes to 1.3×10⁻²⁰.

Measured over one period

Period: 236.8840241
Masses: 1 : 1 : 1
Energy: -1.34315
Angular momentum: 0
Closest approach: 0.002696
Top speed: 19.28
Path length: 617.31
Alignments per period: 240
Stability: unstable (|λ|max 1.1×10¹⁰, published)
Loop closure: 1.3×10⁻²⁰

Neighbours on the map

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