Atlas657 of 3,942

I.A.8

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.8 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 15.606 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 208.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00328 of each other at a top speed of 20.1, line up 34 times a period, and the computed loop closes to 6.4×10⁻²⁶.

Measured over one period

Period: 15.60591907
Masses: 1 : 1 : 0.5
Energy: -1.44516
Angular momentum: 0
Closest approach: 0.003283
Top speed: 20.08
Path length: 43.283
Alignments per period: 34
Topology: aabAbbAABabAABaBBaabAB (free-group class)
Stability: unstable (|λ|max 208.1)
Loop closure: 6.4×10⁻²⁶

Neighbours on the map

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