Atlas2,129 of 3,942

II.C.72

m₃ = 0.75

From Li & Liao (2017)

II.C.72 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 87.507 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 1.737), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000589 of each other at a top speed of 441, line up 114 times a period, and the computed loop closes to 1.6×10⁻²¹.

Measured over one period

Period: 87.50740991
Masses: 1 : 1 : 0.75
Energy: -1.24965
Angular momentum: 0
Closest approach: 5.9×10⁻⁶
Top speed: 440.6
Path length: 185.80
Alignments per period: 114
Topology: ababABababABAbaBABAbabaBAbabABABabABAbabaBABabABABabaBAbabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.737)
Loop closure: 1.6×10⁻²¹

Neighbours on the map

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