Atlas2,165 of 3,942

II.C.246

m₃ = 0.5

From Li & Liao (2017)

II.C.246 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 194.55 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 2.867), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000136 of each other at a top speed of 99, line up 314 times a period, and the computed loop closes to 3.7×10⁻¹⁷.

Measured over one period

Period: 194.5495655
Masses: 1 : 1 : 0.5
Energy: -1.13093
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 99.02
Path length: 462.45
Alignments per period: 314
Topology: ababAbaBABaBABabAbabABabABabABabaBabaBAbaBAbaBAbaBAbabABabABabABabABabABAbABAbaBAbaBAbaBAbaBAbabABabABabABabABabABabaBAbaBAbaBAbaBAbaBABaBABabABabABabABabABabaBAbaBAbaBAbaBAbabAbabABabABabABabaBabABAbABAbaB (free-group class)
Stability: weakly unstable (|λ|max 2.867)
Loop closure: 3.7×10⁻¹⁷

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.