Atlas305 of 3,942

I.A.65

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.65 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 111.34 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 0.00003 of each other at a top speed of 195, line up 194 times a period, and the computed loop closes to 8.2×10⁻²².

Measured over one period

Period: 111.3412553
Masses: 1 : 1 : 0.75
Energy: -1.51907
Angular momentum: 0
Closest approach: 3.0×10⁻⁵
Top speed: 195.2
Path length: 268.54
Alignments per period: 194
Topology: ababABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 8.2×10⁻²²

Neighbours on the map

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