Atlas1,636 of 3,942

II.C.59

m₃ = 2

From Li & Liao (2017)

II.C.59 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 155 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000202 of each other at a top speed of 363, line up 310 times a period, and the computed loop closes to 3.0×10⁻²¹.

Measured over one period

Period: 155.0007437
Masses: 1 : 1 : 2
Energy: -3.25529
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 363.1
Path length: 466.93
Alignments per period: 310
Topology: abababaBABABAbabababABABABabababaBABABAbabababABABABabababaBABABAbabababABABABabababaBABABAbabababABABABabababaBABABAbabababABABABabababABABABAbababaBABABABabababABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.0×10⁻²¹

Neighbours on the map

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