Atlas336 of 3,942

I.A.33

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.33 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 84.014 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 0.0000438 of each other at a top speed of 175, line up 102 times a period, and the computed loop closes to 1.1×10⁻²².

Measured over one period

Period: 84.01438245
Masses: 1 : 1 : 0.5
Energy: -0.945048
Angular momentum: 0
Closest approach: 4.4×10⁻⁵
Top speed: 174.6
Path length: 183.98
Alignments per period: 102
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBBaaBAbbAABaBAbabAbaBAbaBAbaBAbaBAbbAAbaBB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.1×10⁻²²

Neighbours on the map

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