Atlas3,830 of 3,942

Family NF.109

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

Family NF.109 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 66.871 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 268.2), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000102 of each other at a top speed of 313, line up 102 times a period, and the computed loop closes to 4.7×10⁻²¹.

Measured over one period

Period: 66.87059045
Masses: 1 : 1 : 1
Energy: -1.72998
Angular momentum: 0
Closest approach: 1.0×10⁻⁵
Top speed: 313.0
Path length: 183.02
Alignments per period: 102
Topology: abaBAbabABAbabABAbabABabaBABabaBABabaBAbabABAbabABAbaBABabaBAB (free-group class)
Stability: unstable (|λ|max 268.2)
Loop closure: 4.7×10⁻²¹

Neighbours on the map

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