Atlas2,185 of 3,942

II.C.123

m₃ = 0.75

From Li & Liao (2017)

II.C.123 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 144.81 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 1.143), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00019 of each other at a top speed of 77.5, line up 192 times a period, and the computed loop closes to 6.0×10⁻²⁴.

Measured over one period

Period: 144.8128308
Masses: 1 : 1 : 0.75
Energy: -1.27429
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 77.49
Path length: 328.49
Alignments per period: 192
Topology: ababABabaBABabaBABabaBAbabaBAbabABAbabABAbabABababABabaBABabaBABabaBABabaBAbabaBABabABAbabaBAbabABAbabABAbabABAbabAB (free-group class)
Stability: weakly unstable (|λ|max 1.143)
Loop closure: 6.0×10⁻²⁴

Neighbours on the map

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