Atlas575 of 3,942

I.A.19

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.19 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 54.54 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 0.000783 of each other at a top speed of 41.3, line up 70 times a period, and the computed loop closes to 2.8×10⁻¹⁴.

Measured over one period

Period: 54.54019940
Masses: 1 : 1 : 0.5
Energy: -0.996986
Angular momentum: 0
Closest approach: 7.8×10⁻⁴
Top speed: 41.25
Path length: 129.03
Alignments per period: 70
Topology: aaBAbaBAbaBAbabABabABabAAbaBAbaBAbaBABabABabAB (free-group class)
Stability: stable (|λ|max 1.001)
Loop closure: 2.8×10⁻¹⁴

Neighbours on the map

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