Atlas3,213 of 3,942

Choreography NC.141

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

Choreography NC.141 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 284.77 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 11494884045), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0103 of each other at a top speed of 9.86, line up 240 times a period, and the computed loop closes to 1.2×10⁻²¹.

Measured over one period

Period: 284.7744725
Masses: 1 : 1 : 1
Energy: -1.18802
Angular momentum: 0
Closest approach: 0.01032
Top speed: 9.858
Path length: 697.45
Alignments per period: 240
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabAB (free-group class)
Stability: unstable (|λ|max 1.1×10¹⁰, published)
Loop closure: 1.2×10⁻²¹

Neighbours on the map

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