Atlas517 of 3,942

I.A.17

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.17 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 30.508 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 8.958), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00125 of each other at a top speed of 32.6, line up 66 times a period, and the computed loop closes to 7.5×10⁻²⁶.

Measured over one period

Period: 30.50793574
Masses: 1 : 1 : 0.5
Energy: -1.38957
Angular momentum: 0
Closest approach: 0.001247
Top speed: 32.65
Path length: 79.774
Alignments per period: 66
Topology: aabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 8.958)
Loop closure: 7.5×10⁻²⁶

Neighbours on the map

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