Atlas1,517 of 3,942

II.C.37

m₃ = 2

From Li & Liao (2017)

II.C.37 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 96.358 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 39.32), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000142 of each other at a top speed of 137, line up 216 times a period, and the computed loop closes to 3.5×10⁻¹⁷.

Measured over one period

Period: 96.35774546
Masses: 1 : 1 : 2
Energy: -3.52658
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 136.9
Path length: 313.18
Alignments per period: 216
Topology: abababABABAbababaBABABAbababaBABABAbababaBABABabababABABABabababABABABabababABABABabababABABABabababABABABabababABABAB (free-group class)
Stability: unstable (|λ|max 39.32)
Loop closure: 3.5×10⁻¹⁷

Neighbours on the map

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