Atlas648 of 3,942

I.A.8

m₃ = 4

From Li, Jing & Liao (2018)

I.A.8 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 80.638 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 0.0000683 of each other at a top speed of 306, line up 214 times a period, and the computed loop closes to 2.3×10⁻²⁴.

Measured over one period

Period: 80.63815424
Masses: 1 : 1 : 4
Energy: -6.35141
Angular momentum: 0
Closest approach: 6.8×10⁻⁵
Top speed: 306.0
Path length: 327.92
Alignments per period: 214
Topology: ababababababABABABABABAbabababababABABABABABAbabababababABABABABABABabababababaBABABABABABabababababaBABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 2.3×10⁻²⁴

Neighbours on the map

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