Atlas1,429 of 3,942

II.C.56

m₃ = 2

From Li & Liao (2017)

II.C.56 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 186.56 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 5.588), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000172 of each other at a top speed of 125, line up 292 times a period, and the computed loop closes to 3.2×10⁻²⁴.

Measured over one period

Period: 186.5647809
Masses: 1 : 1 : 2
Energy: -2.79182
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 124.7
Path length: 557.83
Alignments per period: 292
Topology: abababABABabababABABabababABABAbababABABAbababABABAbababABABAbababABABAbababABABAbababABABABababABABABababaBABABababaBABABababaBABABababaBABABababaBABABababaBABAB (free-group class)
Stability: weakly unstable (|λ|max 5.588)
Loop closure: 3.2×10⁻²⁴

Neighbours on the map

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