Atlas629 of 3,942

I.A.52

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.52 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 110.33 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 5.868), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00109 of each other at a top speed of 35, line up 126 times a period, and the computed loop closes to 7.0×10⁻²⁵.

Measured over one period

Period: 110.3291692
Masses: 1 : 1 : 0.5
Energy: -0.932025
Angular momentum: 0
Closest approach: 0.001085
Top speed: 35.05
Path length: 255.78
Alignments per period: 126
Topology: aaBAbaBAbabABabAAbaBAbabABabAAbaBAbabABabAAbaBAbaBABabABaaBAbaBABabABaaBAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 5.868)
Loop closure: 7.0×10⁻²⁵

Neighbours on the map

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