Atlas2,119 of 3,942

II.C.129

m₃ = 0.75

From Li & Liao (2017)

II.C.129 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 107.24 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 3.097), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000143 of each other at a top speed of 283, line up 206 times a period, and the computed loop closes to 2.5×10⁻²³.

Measured over one period

Period: 107.2426866
Masses: 1 : 1 : 0.75
Energy: -1.62801
Angular momentum: 0
Closest approach: 1.4×10⁻⁵
Top speed: 282.8
Path length: 271.39
Alignments per period: 206
Topology: ababABababABAbaBABAbabABababABAbaBABAbabABabaBABabaBABabaBABabaBAbabaBAbabABAbabABAbabABAbabABabaBABAbaBABababABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 3.097)
Loop closure: 2.5×10⁻²³

Neighbours on the map

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