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II.C.63

m₃ = 0.75

From Li & Liao (2017)

II.C.63 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 108.13 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 5.231), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00129 of each other at a top speed of 29.7, line up 96 times a period, and the computed loop closes to 8.0×10⁻²⁵.

Measured over one period

Period: 108.1264470
Masses: 1 : 1 : 0.75
Energy: -1.00930
Angular momentum: 0
Closest approach: 0.001287
Top speed: 29.72
Path length: 241.57
Alignments per period: 96
Topology: abaBabaBAbabAbabABabaBabaBAbabAbabABabABabaBAbaBAbaBAbabABabAB (free-group class)
Stability: weakly unstable (|λ|max 5.231)
Loop closure: 8.0×10⁻²⁵

Neighbours on the map

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