Atlas402 of 3,942

I.A.106

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.106 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 105.32 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 unstable (largest Floquet multiplier 208), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000887 of each other at a top speed of 123, line up 230 times a period, and the computed loop closes to 9.6×10⁻²³.

Measured over one period

Period: 105.3228173
Masses: 1 : 1 : 0.5
Energy: -1.39069
Angular momentum: 0
Closest approach: 8.9×10⁻⁵
Top speed: 122.6
Path length: 270.53
Alignments per period: 230
Topology: ababAbABAbaBABaBAbabAbabABaBABabAbabABabABabABAbABabaBabABAbABAbaBabaBAbabAbABABaBabaBAbabAbaBABaBABabAbabABaBABabABabABabaBabABAbABabaBabaBAbABAbaBABaB (free-group class)
Stability: unstable (|λ|max 208.0)
Loop closure: 9.6×10⁻²³

Neighbours on the map

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