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II.C.10

m₃ = 0.75

From Li & Liao (2017)

II.C.10 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 81.338 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 36.42), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00599 of each other at a top speed of 13.8, line up 30 times a period, and the computed loop closes to 8.3×10⁻²⁶.

Measured over one period

Period: 81.33823745
Masses: 1 : 1 : 0.75
Energy: -0.582936
Angular momentum: 0
Closest approach: 0.005994
Top speed: 13.81
Path length: 139.40
Alignments per period: 30
Stability: unstable (|λ|max 36.42)
Loop closure: 8.3×10⁻²⁶

Neighbours on the map

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