Atlas3,210 of 3,942

Choreography NC.135

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

Choreography NC.135 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 245.16 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 1263421), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0275 of each other at a top speed of 6.04, line up 240 times a period, and the computed loop closes to 9.8×10⁻²⁵.

Measured over one period

Period: 245.1609555
Masses: 1 : 1 : 1
Energy: -1.31270
Angular momentum: 0
Closest approach: 0.02750
Top speed: 6.040
Path length: 632.66
Alignments per period: 240
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 1.3×10⁶, published)
Loop closure: 9.8×10⁻²⁵

Neighbours on the map

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