Atlas2,017 of 3,942

II.C.164

m₃ = 0.75

From Li & Liao (2017)

II.C.164 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 142.55 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 18.69), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000356 of each other at a top speed of 179, line up 348 times a period, and the computed loop closes to 2.0×10⁻²².

Measured over one period

Period: 142.5493314
Masses: 1 : 1 : 0.75
Energy: -1.91364
Angular momentum: 0
Closest approach: 3.6×10⁻⁵
Top speed: 179.1
Path length: 384.15
Alignments per period: 348
Topology: ababAbabaBABabABABabaBAbabaBAbabABABabABAbabABababABAbaBABAbaBABababAbabaBABabABABabaBAbabaBABabABABabABAbabaBAbabABABabABAbabaBababABAbaBABAbaBABababABabaBABabABABabaBAbabaBAbabABABabABAbabaBababABAbaBABAbaBAB (free-group class)
Stability: unstable (|λ|max 18.69)
Loop closure: 2.0×10⁻²²

Neighbours on the map

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