Why Phi? – Moons of Pluto

See main post for details [image credit: Wikipedia / WolfmanSF]

In this extract from Wikipedia we’ve highlighted the relevant part in bold, so without more ado:

Resonances
Styx, Nix, and Hydra are in a 3-body orbital resonance with orbital periods in a ratio of 18:22:33. The ratios are exact when orbital precession is taken into account. This means that in a recurring cycle there are 11 orbits of Styx for every 9 of Nix and 6 of Hydra. Nix and Hydra are in a simple 2:3 resonance. The ratios of synodic periods are such that there are 5 Styx–Hydra conjunctions and 3 Nix–Hydra conjunctions for every 2 conjunctions of Styx and Nix.

As with the Laplace resonance of the Galilean satellites of Jupiter, triple conjunctions never occur.

Source: Moons of Pluto – Wikipedia.

Note that 2,3, and 5 are Fibonacci numbers, supporting our ‘Why Phi?’ concept.

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Full caption for the diagram* from Wikipedia [* click to enlarge]:
‘This series of diagrams depicts one cycle of the movements of Pluto’s moons Hydra (blue), Nix (red) and Styx (black), as controlled by their mutual orbital resonance. The view is from the north pole of the system, and all motions are counterclockwise. The movements shown are actually a composite of orbital motion and orbital precession. Libration is disregarded. The time interval between diagrams is half of Hydra’s orbital period (equivalent to 0.75 Nix periods, or 0.917 Styx periods).

Numbers in the upper right corners of diagrams indicate the number of orbits completed by each moon since the first diagram (a full cycle consists of 6 Hydra orbits, 9 Nix orbits, and 11 Styx orbits, and would be represented by a return to the first diagram). The figure shows all of the conjunctions and oppositions of Nix and Hydra, and of Nix and Styx, but only one fifth of those between Hydra and Styx (notice that there are no triple conjunctions). All orbits in the Pluto system are shown to scale, but sizes of moons are not.

The diagrams were created using Wolfram Mathematica according to the results reported in Showalter, M. R.; Hamilton, D. P. (3 June 2015). “Resonant interactions and chaotic rotation of Pluto’s small moons”. Nature 522 (7554): 45–49. doi:10.1038/nature14469.’