Atlas519 of 3,942

I.A.32

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.32 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 49.168 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 4.799), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000788 of each other at a top speed of 41.1, line up 102 times a period, and the computed loop closes to 9.5×10⁻²⁵.

Measured over one period

Period: 49.16752626
Masses: 1 : 1 : 0.5
Energy: -1.35074
Angular momentum: 0
Closest approach: 7.9×10⁻⁴
Top speed: 41.14
Path length: 128.76
Alignments per period: 102
Topology: aabAbaBAbaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 4.799)
Loop closure: 9.5×10⁻²⁵

Neighbours on the map

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