Atlas539 of 3,942

I.A.63

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.63 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 112.37 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 0.000147 of each other at a top speed of 95.1, line up 154 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 112.3665491
Masses: 1 : 1 : 0.5
Energy: -1.03227
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 95.12
Path length: 266.86
Alignments per period: 154
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.6×10⁻²⁴

Neighbours on the map

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