Atlas2,079 of 3,942

II.C.162

m₃ = 0.75

From Li & Liao (2017)

II.C.162 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 162.45 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 2.891), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000398 of each other at a top speed of 169, line up 330 times a period, and the computed loop closes to 3.1×10⁻²³.

Measured over one period

Period: 162.4518901
Masses: 1 : 1 : 0.75
Energy: -1.68645
Angular momentum: 0
Closest approach: 4.0×10⁻⁵
Top speed: 169.4
Path length: 414.09
Alignments per period: 330
Topology: ababABababABAbaBABAbabABababABAbaBABAbabABababABabaBABAbaBABababABabaBABAbaBABAbabABababABAbaBABAbabABababABabaBABAbaBABababABabaBABAbaBABababABababABAbaBABAbabABababABAbaBABAbaBABababABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 2.891)
Loop closure: 3.1×10⁻²³

Neighbours on the map

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