Atlas439 of 3,942

I.A.68

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.68 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 83.847 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 0.00011 of each other at a top speed of 11, line up 158 times a period, and the computed loop closes to 5.3×10⁻¹⁷.

Measured over one period

Period: 83.84729076
Masses: 1 : 1 : 0.5
Energy: -1.25662
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 110.2
Path length: 208.22
Alignments per period: 158
Topology: abaBabaBAbABAbaBAbabAbaBABaBABabAbabABabABabABabaBabABAbABAbaBabaBAbaBABaBAbabAbabABaBABabABabABabABAbAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 5.3×10⁻¹⁷

Neighbours on the map

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