Atlas579 of 3,942

I.A.72

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.72 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 115.55 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 125.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000825 of each other at a top speed of 40.2, line up 154 times a period, and the computed loop closes to 8.4×10⁻²⁵.

Measured over one period

Period: 115.5464074
Masses: 1 : 1 : 0.5
Energy: -1.03550
Angular momentum: 0
Closest approach: 8.2×10⁻⁴
Top speed: 40.21
Path length: 283.13
Alignments per period: 154
Topology: aaBAbabABabAAbaBAbabABabAAbaBAbabABabAAbaBAbabABabAAbaBABabABaaBAbaBABabABaaBAbaBABabABaaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 125.3)
Loop closure: 8.4×10⁻²⁵

Neighbours on the map

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