Atlas1,717 of 3,942

II.C.72

m₃ = 2

From Li & Liao (2017)

II.C.72 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 139.94 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 1.195), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000579 of each other at a top speed of 215, line up 356 times a period, and the computed loop closes to 5.6×10⁻¹⁶.

Measured over one period

Period: 139.9401650
Masses: 1 : 1 : 2
Energy: -3.81124
Angular momentum: 0
Closest approach: 5.8×10⁻⁵
Top speed: 214.6
Path length: 440.06
Alignments per period: 356
Topology: ababababABABABAbababaBABABABabababaBABABABabababABABABAbabababABABABAbabababABABABAbabababABABABAbababaBABABABabababaBABABABabababaBABABABabababaBABABABabababABABABAbabababABABABAbababaBABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.195)
Loop closure: 5.6×10⁻¹⁶

Neighbours on the map

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