Atlas1,771 of 3,942

II.C.217

m₃ = 0.5

From Li & Liao (2017)

II.C.217 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 125.48 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 1.694), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000139 of each other at a top speed of 309, line up 250 times a period, and the computed loop closes to 1.3×10⁻²².

Measured over one period

Period: 125.4822944
Masses: 1 : 1 : 0.5
Energy: -1.31125
Angular momentum: 0
Closest approach: 1.4×10⁻⁵
Top speed: 309.4
Path length: 325.07
Alignments per period: 250
Topology: ababAbABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabAbaBABaBABabAbabABabABabABabABabABabABabaBaBABAbAbabABabABabABabABabABabABabaBabABAbABAbaBabaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABaB (free-group class)
Stability: weakly unstable (|λ|max 1.694)
Loop closure: 1.3×10⁻²²

Neighbours on the map

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