Atlas675 of 3,942

I.A.10

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.10 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 22.877 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 unstable (largest Floquet multiplier 131.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0039 of each other at a top speed of 18.5, line up 34 times a period, and the computed loop closes to 2.7×10⁻²⁶.

Measured over one period

Period: 22.87703895
Masses: 1 : 1 : 0.5
Energy: -1.22339
Angular momentum: 0
Closest approach: 0.003897
Top speed: 18.54
Path length: 64.732
Alignments per period: 34
Topology: aaaaabABabAAAAABabAB (free-group class)
Stability: unstable (|λ|max 131.3)
Loop closure: 2.7×10⁻²⁶

Neighbours on the map

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