Atlas587 of 3,942

I.A.71

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.71 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 129.01 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 4.968), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000806 of each other at a top speed of 40.7, line up 158 times a period, and the computed loop closes to 6.9×10⁻²⁵.

Measured over one period

Period: 129.0111011
Masses: 1 : 1 : 0.5
Energy: -0.964538
Angular momentum: 0
Closest approach: 8.1×10⁻⁴
Top speed: 40.67
Path length: 299.33
Alignments per period: 158
Topology: aaBAbaBAbaBAbabABabABabAAbaBAbaBAbaBABabABabABabABabAAbaBAbaBAbaBABabABabABaaBAbaBAbaBAbabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 4.968)
Loop closure: 6.9×10⁻²⁵

Neighbours on the map

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