Atlas2,074 of 3,942

II.C.139

m₃ = 0.75

From Li & Liao (2017)

II.C.139 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 110.89 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 0.00000151 of each other at a top speed of 871, line up 238 times a period, and the computed loop closes to 7.8×10⁻²⁰.

Measured over one period

Period: 110.8909227
Masses: 1 : 1 : 0.75
Energy: -1.74326
Angular momentum: 0
Closest approach: 1.5×10⁻⁶
Top speed: 870.7
Path length: 280.82
Alignments per period: 238
Topology: ababABababABAbabABAbabaBAbabABABabaBAbabaBABabaBABababABababABAbaBABAbabABababABAbabABAbabaBAbabABABabABABabaBAbabaBABabaBABababABabaBABAbaBAB (free-group class)
Stability: stable (|λ|max 1.001)
Loop closure: 7.8×10⁻²⁰

Neighbours on the map

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