Atlas617 of 3,942

I.A.48

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.48 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 103.64 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 7.309), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00114 of each other at a top speed of 34.2, line up 122 times a period, and the computed loop closes to 6.7×10⁻²⁵.

Measured over one period

Period: 103.6411579
Masses: 1 : 1 : 0.5
Energy: -0.943353
Angular momentum: 0
Closest approach: 0.001138
Top speed: 34.21
Path length: 239.20
Alignments per period: 122
Topology: aaBAbaBAbabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBABabABabABaaBAbaBAbaBABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 7.309)
Loop closure: 6.7×10⁻²⁵

Neighbours on the map

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