Atlas1,842 of 3,942

II.C.111

m₃ = 0.75

From Li & Liao (2017)

II.C.111 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 68.425 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 427.9), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000493 of each other at a top speed of 152, line up 168 times a period, and the computed loop closes to 2.6×10⁻²³.

Measured over one period

Period: 68.42513420
Masses: 1 : 1 : 0.75
Energy: -1.92766
Angular momentum: 0
Closest approach: 4.9×10⁻⁵
Top speed: 152.2
Path length: 190.83
Alignments per period: 168
Topology: ababAbabaBababABAbaBABAbabABababABabaBABabABABabABAbabABababABabaBABabABABabABAbabABababABabaBABAbaBAB (free-group class)
Stability: unstable (|λ|max 427.9)
Loop closure: 2.6×10⁻²³

Neighbours on the map

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