Atlas3,767 of 3,942

Family NF.56

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

Family NF.56 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 25.945 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 2429), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000482 of each other at a top speed of 45.6, line up 70 times a period, and the computed loop closes to 1.3×10⁻²⁵.

Measured over one period

Period: 25.94528876
Masses: 1 : 1 : 1
Energy: -2.44668
Angular momentum: 0
Closest approach: 4.8×10⁻⁴
Top speed: 45.56
Path length: 77.671
Alignments per period: 70
Topology: aabaBABAbabABABabaBABAbabbaBAABababABBAb (free-group class)
Stability: unstable (|λ|max 2429)
Loop closure: 1.3×10⁻²⁵

Neighbours on the map

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