Atlas639 of 3,942

I.A.42

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.42 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 55.478 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 40.64), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00178 of each other at a top speed of 27.4, line up 118 times a period, and the computed loop closes to 4.3×10⁻²⁶.

Measured over one period

Period: 55.47840143
Masses: 1 : 1 : 0.5
Energy: -1.38796
Angular momentum: 0
Closest approach: 0.001777
Top speed: 27.37
Path length: 148.71
Alignments per period: 118
Topology: aabAbaBABaBABabAbaaBBabAAbbAAbaBBaabAbbAABaBAbabAbabABaBAAbbABaaBBaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 40.64)
Loop closure: 4.3×10⁻²⁶

Neighbours on the map

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