Atlas3,744 of 3,942

Family NF.52

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

Family NF.52 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 27.208 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 29753), so a small nudge makes it unravel over a few periods. The bodies pass within 0.012 of each other at a top speed of 9.25, line up 70 times a period, and the computed loop closes to 6.1×10⁻²⁵.

Measured over one period

Period: 27.20769467
Masses: 1 : 1 : 1
Energy: -2.36827
Angular momentum: 0
Closest approach: 0.01195
Top speed: 9.246
Path length: 77.008
Alignments per period: 70
Topology: aabABABababABABabbaBAABabbaBABAbaabABBAb (free-group class)
Stability: unstable (|λ|max 29753)
Loop closure: 6.1×10⁻²⁵

Neighbours on the map

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