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II.C.43

m₃ = 0.75

From Li & Liao (2017)

II.C.43 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 84.691 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00297 of each other at a top speed of 19.6, line up 70 times a period, and the computed loop closes to 3.5×10⁻²⁵.

Measured over one period

Period: 84.69113300
Masses: 1 : 1 : 0.75
Energy: -1.00289
Angular momentum: 0
Closest approach: 0.002971
Top speed: 19.61
Path length: 188.85
Alignments per period: 70
Stability: stable (|λ|max 1.000)
Loop closure: 3.5×10⁻²⁵

Neighbours on the map

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