Atlas703 of 3,942

I.A.11

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.11 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 42.8 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 6.589), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00484 of each other at a top speed of 15.3, line up 50 times a period, and the computed loop closes to 8.7×10⁻²⁶.

Measured over one period

Period: 42.80044884
Masses: 1 : 1 : 0.75
Energy: -1.20709
Angular momentum: 0
Closest approach: 0.004844
Top speed: 15.34
Path length: 103.08
Alignments per period: 50
Topology: abaBAbaBAbabABabABAbaBAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 6.589)
Loop closure: 8.7×10⁻²⁶

Neighbours on the map

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