Atlas3,781 of 3,942

Family NF.105

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

Family NF.105 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 51.859 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 2201), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00108 of each other at a top speed of 30.5, line up 98 times a period, and the computed loop closes to 6.4×10⁻²⁵.

Measured over one period

Period: 51.85927756
Masses: 1 : 1 : 1
Energy: -2.00133
Angular momentum: 0
Closest approach: 0.001077
Top speed: 30.54
Path length: 152.43
Alignments per period: 98
Topology: ababABababABabaBABabABabaBABabABAbabaBABabABAbabABabABAbabAB (free-group class)
Stability: unstable (|λ|max 2201)
Loop closure: 6.4×10⁻²⁵

Neighbours on the map

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