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Family NF.54

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2022)

Family NF.54 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 27.58 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2022). Orbits from topological families that no earlier catalogue contained; all of them unstable. It is unstable (largest Floquet multiplier 16719), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0106 of each other at a top speed of 9.77, line up 70 times a period, and the computed loop closes to 5.4×10⁻²⁵.

Measured over one period

Period: 27.57952650
Masses: 1 : 1 : 1
Energy: -2.34878
Angular momentum: 0
Closest approach: 0.01058
Top speed: 9.767
Path length: 76.430
Alignments per period: 70
Topology: aabABABababABABabbaBAABababABABababABBAb (free-group class)
Stability: unstable (|λ|max 16719)
Loop closure: 5.4×10⁻²⁵

Neighbours on the map

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