Atlas3,805 of 3,942

Family NF.76

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

Family NF.76 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 42.805 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 5943), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00112 of each other at a top speed of 29.9, line up 78 times a period, and the computed loop closes to 8.6×10⁻²⁵.

Measured over one period

Period: 42.80482672
Masses: 1 : 1 : 1
Energy: -1.95756
Angular momentum: 0
Closest approach: 0.001124
Top speed: 29.94
Path length: 124.00
Alignments per period: 78
Topology: ababABababABabaBABabaBAbaBABabABAbaBAbabABAbabAB (free-group class)
Stability: unstable (|λ|max 5943)
Loop closure: 8.6×10⁻²⁵

Neighbours on the map

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