Atlas549 of 3,942

I.A.112

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.112 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 110.25 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 7.099), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000109 of each other at a top speed of 111, line up 234 times a period, and the computed loop closes to 7.5×10⁻²⁴.

Measured over one period

Period: 110.2475386
Masses: 1 : 1 : 0.5
Energy: -1.37174
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 110.8
Path length: 288.38
Alignments per period: 234
Topology: aabAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 7.099)
Loop closure: 7.5×10⁻²⁴

Neighbours on the map

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