Atlas492 of 3,942

I.A.81

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.81 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 117.92 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 11.12), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000683 of each other at a top speed of 44.2, line up 178 times a period, and the computed loop closes to 8.7×10⁻²⁵.

Measured over one period

Period: 117.9225114
Masses: 1 : 1 : 0.5
Energy: -1.09977
Angular momentum: 0
Closest approach: 6.8×10⁻⁴
Top speed: 44.17
Path length: 288.41
Alignments per period: 178
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 11.12)
Loop closure: 8.7×10⁻²⁵

Neighbours on the map

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