Atlas277 of 3,942

I.A.108

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.108 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 186.9 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 1.677), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000129 of each other at a top speed of 322, line up 234 times a period, and the computed loop closes to 3.0×10⁻²².

Measured over one period

Period: 186.8989238
Masses: 1 : 1 : 0.5
Energy: -0.948917
Angular momentum: 0
Closest approach: 1.3×10⁻⁵
Top speed: 322.1
Path length: 390.59
Alignments per period: 234
Topology: ababAbabABaBABabABAbaBabaBAbabABaBABabABAbABabaBAbabAbaBABabABAbABabaBababAbABABaBABabAbabABabaBAbABAbaBABabAbabABabaBabABAbaBABaBAbabABabaBabABAbABABaB (free-group class)
Stability: weakly unstable (|λ|max 1.677)
Loop closure: 3.0×10⁻²²

Neighbours on the map

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