Atlas413 of 3,942

I.A.59

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.59 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 110.74 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 0.0000837 of each other at a top speed of 117, line up 178 times a period, and the computed loop closes to 3.8×10⁻²⁴.

Measured over one period

Period: 110.7390746
Masses: 1 : 1 : 0.75
Energy: -1.45246
Angular momentum: 0
Closest approach: 8.4×10⁻⁵
Top speed: 116.8
Path length: 271.84
Alignments per period: 178
Topology: abaBAbabABAbabABAbabABabaBABabaBABabaBAbabABAbabABAbabABAbaBABabaBABabaBABabABAbabABAbabABAbaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.8×10⁻²⁴

Neighbours on the map

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