Atlas619 of 3,942

I.A.111

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.111 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 180.3 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 weakly unstable (largest Floquet multiplier 2.109), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000745 of each other at a top speed of 134, line up 226 times a period, and the computed loop closes to 3.4×10⁻²³.

Measured over one period

Period: 180.3047709
Masses: 1 : 1 : 0.5
Energy: -0.985122
Angular momentum: 0
Closest approach: 7.5×10⁻⁵
Top speed: 133.8
Path length: 426.21
Alignments per period: 226
Topology: aaBAbaBAbabABabABaaBAbaBAbaBABabABabAAbaBAbaBAbabABabABaaBAbaBAbabABabABabAAbaBAbaBABabABabAAbaBAbaBAbabABabABaaBAbaBAbaBABabABabAAbaBAbaBABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 2.109)
Loop closure: 3.4×10⁻²³

Neighbours on the map

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