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II.C.3

m₃ = 0.75

From Li & Liao (2017)

II.C.3 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 24.224 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 42.93), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0329 of each other at a top speed of 5.54, line up 26 times a period, and the computed loop closes to 1.6×10⁻²⁸.

Measured over one period

Period: 24.22444800
Masses: 1 : 1 : 0.75
Energy: -1.20667
Angular momentum: 0
Closest approach: 0.03292
Top speed: 5.536
Path length: 59.232
Alignments per period: 26
Stability: unstable (|λ|max 42.93)
Loop closure: 1.6×10⁻²⁸

Neighbours on the map

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