Atlas578 of 3,942

I.A.13

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.13 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 39.285 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 8574), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00678 of each other at a top speed of 14, line up 58 times a period, and the computed loop closes to 1.3×10⁻²⁵.

Measured over one period

Period: 39.28491779
Masses: 1 : 1 : 0.5
Energy: -1.09808
Angular momentum: 0
Closest approach: 0.006781
Top speed: 14.02
Path length: 97.873
Alignments per period: 58
Topology: aaBAbaBAbaBAbabABabAAbaBAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 8574)
Loop closure: 1.3×10⁻²⁵

Neighbours on the map

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