Atlas688 of 3,942

I.A.13

m₃ = 4

From Li, Jing & Liao (2018)

I.A.13 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 127.02 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 0.0000684 of each other at a top speed of 306, line up 290 times a period, and the computed loop closes to 9.9×10⁻²³.

Measured over one period

Period: 127.0151386
Masses: 1 : 1 : 4
Energy: -5.74887
Angular momentum: 0
Closest approach: 6.8×10⁻⁵
Top speed: 305.8
Path length: 496.50
Alignments per period: 290
Topology: abababababaBABABABABAbabababababABABABABABAbabababababABABABABABAbabababababABABABABABAbababababaBABABABABABabababababaBABABABABABabababababaBABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 9.9×10⁻²³

Neighbours on the map

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