Atlas429 of 3,942

I.A.110

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.110 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 116.7 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 1.382), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000236 of each other at a top speed of 75.1, line up 238 times a period, and the computed loop closes to 6.4×10⁻¹⁸.

Measured over one period

Period: 116.6973087
Masses: 1 : 1 : 0.5
Energy: -1.32121
Angular momentum: 0
Closest approach: 2.4×10⁻⁴
Top speed: 75.13
Path length: 296.22
Alignments per period: 238
Topology: ababAbaBABaBABabAbabABabABabABAbaBabaBAbaBAbaBABaBAbabABabABabABAbABabaBabaBAbABABaBAbabAbabABaBABabABabABabaBAbABAbaBAbaBAbabAbaBABabABabABabaBabABAbABAbaB (free-group class)
Stability: weakly unstable (|λ|max 1.382)
Loop closure: 6.4×10⁻¹⁸

Neighbours on the map

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