Atlas493 of 3,942

I.A.123

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.123 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 179.74 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 1.001), so a small nudge only makes it wobble. The bodies pass within 0.000357 of each other at a top speed of 61.1, line up 262 times a period, and the computed loop closes to 1.4×10⁻¹³.

Measured over one period

Period: 179.7442887
Masses: 1 : 1 : 0.5
Energy: -1.07216
Angular momentum: 0
Closest approach: 3.6×10⁻⁴
Top speed: 61.12
Path length: 432.77
Alignments per period: 262
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.001)
Loop closure: 1.4×10⁻¹³

Neighbours on the map

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