Atlas3,736 of 3,942

Family NF.110

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

Family NF.110 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 50.683 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 889.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00002 of each other at a top speed of 224, line up 110 times a period, and the computed loop closes to 2.8×10⁻²¹.

Measured over one period

Period: 50.68324749
Masses: 1 : 1 : 1
Energy: -2.14487
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 224.0
Path length: 142.40
Alignments per period: 110
Topology: ababABAbabaBABababABABabaBABababABABabaBABAbabABABababABAbabABAB (free-group class)
Stability: unstable (|λ|max 889.3)
Loop closure: 2.8×10⁻²¹

Neighbours on the map

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