Atlas3,258 of 3,942

Choreography NC.154

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

Choreography NC.154 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 213.61 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 11767498), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000761 of each other at a top speed of 36.3, line up 270 times a period, and the computed loop closes to 3.2×10⁻²².

Measured over one period

Period: 213.6076281
Masses: 1 : 1 : 1
Energy: -1.55451
Angular momentum: 0
Closest approach: 7.6×10⁻⁴
Top speed: 36.29
Path length: 573.75
Alignments per period: 270
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.2×10⁷, published)
Loop closure: 3.2×10⁻²²

Neighbours on the map

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