Atlas2,068 of 3,942

II.C.114

m₃ = 0.75

From Li & Liao (2017)

II.C.114 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 86.202 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 1.001), so a small nudge only makes it wobble. The bodies pass within 0.0000292 of each other at a top speed of 198, line up 178 times a period, and the computed loop closes to 1.2×10⁻²².

Measured over one period

Period: 86.20184841
Masses: 1 : 1 : 0.75
Energy: -1.69677
Angular momentum: 0
Closest approach: 2.9×10⁻⁵
Top speed: 197.8
Path length: 214.97
Alignments per period: 178
Topology: ababABababABAbabABAbabABAbabABABabaBABabaBABabaBABababABababABAbabABAbabABAbabABABabABABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.001)
Loop closure: 1.2×10⁻²²

Neighbours on the map

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