Atlas576 of 3,942

I.A.82

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.82 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 124.49 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 unstable (largest Floquet multiplier 30.07), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00139 of each other at a top speed of 31, line up 174 times a period, and the computed loop closes to 6.0×10⁻²⁵.

Measured over one period

Period: 124.4856938
Masses: 1 : 1 : 0.5
Energy: -1.05881
Angular momentum: 0
Closest approach: 0.001387
Top speed: 30.98
Path length: 304.80
Alignments per period: 174
Topology: aaBAbaBAbabABabABabAAbaBAbaBAbabABabAAbaBAbaBAbabABabABabAAbaBAbaBABabABabABaaBAbaBAbaBABabABaaBAbaBAbaBABabABabAB (free-group class)
Stability: unstable (|λ|max 30.07)
Loop closure: 6.0×10⁻²⁵

Neighbours on the map

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