Atlas520 of 3,942

I.A.73

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.73 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 82.319 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 5.121), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000611 of each other at a top speed of 148, line up 162 times a period, and the computed loop closes to 3.4×10⁻²³.

Measured over one period

Period: 82.31944212
Masses: 1 : 1 : 0.5
Energy: -1.30378
Angular momentum: 0
Closest approach: 6.1×10⁻⁵
Top speed: 147.7
Path length: 212.94
Alignments per period: 162
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbAAbaBBaabAbbAABaBAbabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 5.121)
Loop closure: 3.4×10⁻²³

Neighbours on the map

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