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II.C.23

m₃ = 0.75

From Li & Liao (2017)

II.C.23 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 56.583 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 200), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00925 of each other at a top speed of 11.2, line up 48 times a period, and the computed loop closes to 7.4×10⁻²⁶.

Measured over one period

Period: 56.58344581
Masses: 1 : 1 : 0.75
Energy: -1.00957
Angular momentum: 0
Closest approach: 0.009246
Top speed: 11.16
Path length: 131.13
Alignments per period: 48
Stability: unstable (|λ|max 200.0)
Loop closure: 7.4×10⁻²⁶

Neighbours on the map

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