Atlas2,166 of 3,942

II.C.225

m₃ = 0.5

From Li & Liao (2017)

II.C.225 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 165.09 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 3.408), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000272 of each other at a top speed of 70, line up 264 times a period, and the computed loop closes to 1.4×10⁻²⁴.

Measured over one period

Period: 165.0883446
Masses: 1 : 1 : 0.5
Energy: -1.12726
Angular momentum: 0
Closest approach: 2.7×10⁻⁴
Top speed: 70.01
Path length: 394.56
Alignments per period: 264
Topology: ababAbaBABaBAbabAbabABaBABabABabABabABabABabaBabaBAbaBAbaBAbaBAbaBAbaBAbabAbabABabABabABabABabABabABabaBabaBAbaBAbaBAbaBAbaBAbaBAbabAbabABabABabABabABabABAbABabaBabaBAbABAbaB (free-group class)
Stability: weakly unstable (|λ|max 3.408)
Loop closure: 1.4×10⁻²⁴

Neighbours on the map

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