Atlas2,080 of 3,942

II.C.118

m₃ = 0.75

From Li & Liao (2017)

II.C.118 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 94.477 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 2.584), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000122 of each other at a top speed of 96.7, line up 190 times a period, and the computed loop closes to 4.4×10⁻²⁴.

Measured over one period

Period: 94.47667092
Masses: 1 : 1 : 0.75
Energy: -1.67534
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 96.71
Path length: 239.39
Alignments per period: 190
Topology: ababABababABAbaBABAbabABababABAbaBABAbabABababABAbaBABAbabABababABabaBABAbaBABababABabaBABAbaBABababABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 2.584)
Loop closure: 4.4×10⁻²⁴

Neighbours on the map

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