Atlas337 of 3,942

I.A.115

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.115 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 179.38 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 1.968), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000317 of each other at a top speed of 64.8, line up 242 times a period, and the computed loop closes to 6.0×10⁻²⁴.

Measured over one period

Period: 179.3796184
Masses: 1 : 1 : 0.5
Energy: -1.00848
Angular momentum: 0
Closest approach: 3.2×10⁻⁴
Top speed: 64.82
Path length: 404.84
Alignments per period: 242
Topology: ababAbaBABaBAbabAbabABaBABabABabABabABabABabABabABabABAbABabaBabaBAbABAbaBababAbABABaBAbabAbaBABaBABabAbabABabABabABabABabABabABabABabaBabABAbABAbaBabaBAbABABaB (free-group class)
Stability: weakly unstable (|λ|max 1.968)
Loop closure: 6.0×10⁻²⁴

Neighbours on the map

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