Atlas1,577 of 3,942

II.C.39

m₃ = 2

From Li & Liao (2017)

II.C.39 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 97.992 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 3.476), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000203 of each other at a top speed of 115, line up 232 times a period, and the computed loop closes to 2.9×10⁻¹⁷.

Measured over one period

Period: 97.99245019
Masses: 1 : 1 : 2
Energy: -3.64702
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 114.6
Path length: 316.09
Alignments per period: 232
Topology: abababaBABABAbabababABABABabababABABABAbababaBABABAbabababABABABabababABABABabababABABABabababaBABABAbababaBABABABabababABABAB (free-group class)
Stability: weakly unstable (|λ|max 3.476)
Loop closure: 2.9×10⁻¹⁷

Neighbours on the map

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