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II.C.20

m₃ = 0.75

From Li & Liao (2017)

II.C.20 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 26.1 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 41.14), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00257 of each other at a top speed of 21, line up 50 times a period, and the computed loop closes to 1.2×10⁻²⁶.

Measured over one period

Period: 26.09969970
Masses: 1 : 1 : 0.75
Energy: -1.67820
Angular momentum: 0
Closest approach: 0.002569
Top speed: 20.99
Path length: 75.040
Alignments per period: 50
Stability: unstable (|λ|max 41.14)
Loop closure: 1.2×10⁻²⁶

Neighbours on the map

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