Atlas556 of 3,942

I.A.3

m₃ = 8

From Li, Jing & Liao (2018)

I.A.3 m₃ = 8 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 8 that return to their starting positions and velocities every 153.38 time units, published by Li, Jing & Liao (2018). Class I.A orbits found with Liao’s clean numerical simulation method, for a third body of varying mass. It is weakly unstable (largest Floquet multiplier 2.790), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000157 of each other at a top speed of 952, line up 674 times a period, and the computed loop closes to 2.9×10⁻²³.

Measured over one period

Period: 153.3805946
Masses: 1 : 1 : 8
Energy: -14.2532
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 951.5
Path length: 854.84
Alignments per period: 674
Topology: ababababababababababababaBABABABABABABABABABABABAbababababababababababababABABABABABABABABABABABABababababababababababababAbABABABABABABABABABABABABababababababababababababABABABABABABABABABABABABAbabababababababababababaBABABABABABABABABABABABABababababababababababababABABABABABABABABABABABABaBababababababababababababABABABABABABABABABABABAB (free-group class)
Stability: weakly unstable (|λ|max 2.790)
Loop closure: 2.9×10⁻²³

Neighbours on the map

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