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II.C.2

m₃ = 0.75

From Li & Liao (2017)

II.C.2 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 36.193 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 3711), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00615 of each other at a top speed of 12.9, line up 20 times a period, and the computed loop closes to 2.2×10⁻²⁶.

Measured over one period

Period: 36.19343923
Masses: 1 : 1 : 0.75
Energy: -0.777386
Angular momentum: 0
Closest approach: 0.006151
Top speed: 12.91
Path length: 63.327
Alignments per period: 20
Stability: unstable (|λ|max 3711)
Loop closure: 2.2×10⁻²⁶

Neighbours on the map

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