Atlas2,123 of 3,942

II.C.106

m₃ = 0.75

From Li & Liao (2017)

II.C.106 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 78.958 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 1.135), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000186 of each other at a top speed of 78.3, line up 160 times a period, and the computed loop closes to 9.6×10⁻²⁵.

Measured over one period

Period: 78.95750618
Masses: 1 : 1 : 0.75
Energy: -1.68380
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 78.34
Path length: 200.65
Alignments per period: 160
Topology: ababABababABAbaBABAbabABababABAbaBABAbabABababABAbaBABAbaBABababABabaBABAbaBABababABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.135)
Loop closure: 9.6×10⁻²⁵

Neighbours on the map

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