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Family NF.97

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

Family NF.97 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 45.124 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 3132), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0117 of each other at a top speed of 9.41, line up 92 times a period, and the computed loop closes to 4.1×10⁻²⁵.

Measured over one period

Period: 45.12385915
Masses: 1 : 1 : 1
Energy: -2.10066
Angular momentum: 0
Closest approach: 0.01170
Top speed: 9.407
Path length: 135.28
Alignments per period: 92
Topology: ababABAbaBABababABAbaBABabABAbaBABababABAbaBABabABAbaBAB (free-group class)
Stability: unstable (|λ|max 3132)
Loop closure: 4.1×10⁻²⁵

Neighbours on the map

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