Atlas3,761 of 3,942

Family NF.78

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

Family NF.78 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 31.932 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 13287), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00125 of each other at a top speed of 28.4, line up 84 times a period, and the computed loop closes to 9.8×10⁻²⁵.

Measured over one period

Period: 31.93224089
Masses: 1 : 1 : 1
Energy: -2.40364
Angular momentum: 0
Closest approach: 0.001248
Top speed: 28.36
Path length: 90.672
Alignments per period: 84
Topology: aabABABababABBAbaabABABabbaBAABababABABabbaBABAb (free-group class)
Stability: unstable (|λ|max 13287)
Loop closure: 9.8×10⁻²⁵

Neighbours on the map

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