Atlas644 of 3,942

I.A.9

m₃ = 4

From Li, Jing & Liao (2018)

I.A.9 m₃ = 4 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 4 that return to their starting positions and velocities every 89.257 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000903 of each other at a top speed of 266, line up 222 times a period, and the computed loop closes to 4.7×10⁻¹⁷.

Measured over one period

Period: 89.25701358
Masses: 1 : 1 : 4
Energy: -6.07836
Angular momentum: 0
Closest approach: 9.0×10⁻⁵
Top speed: 266.2
Path length: 349.44
Alignments per period: 222
Topology: ababababababABABABABABAbabababababaBABABABABABababababababABABABABABABabababababaBABABABABABAbabababababABABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 4.7×10⁻¹⁷

Neighbours on the map

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