Atlas333 of 3,942

I.A.101

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.101 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 180.18 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 3.168), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000042 of each other at a top speed of 178, line up 222 times a period, and the computed loop closes to 2.6×10⁻²².

Measured over one period

Period: 180.1794836
Masses: 1 : 1 : 0.5
Energy: -0.954340
Angular momentum: 0
Closest approach: 4.2×10⁻⁵
Top speed: 178.2
Path length: 397.37
Alignments per period: 222
Topology: aabAbaBAbaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbabAbaBAbaBAbaBAbaBAbbAAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBABaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 3.168)
Loop closure: 2.6×10⁻²²

Neighbours on the map

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