Atlas2,194 of 3,942

II.C.32

m₃ = 0.75

From Li & Liao (2017)

II.C.32 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 56.081 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 204.2), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00147 of each other at a top speed of 27.9, line up 66 times a period, and the computed loop closes to 2.9×10⁻²⁵.

Measured over one period

Period: 56.08087861
Masses: 1 : 1 : 0.75
Energy: -1.18006
Angular momentum: 0
Closest approach: 0.001467
Top speed: 27.93
Path length: 120.13
Alignments per period: 66
Topology: ababAbabaBababABAbaBABAbabABabaBABAbaBAB (free-group class)
Stability: unstable (|λ|max 204.2)
Loop closure: 2.9×10⁻²⁵

Neighbours on the map

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