# Why Phi? – Saturn’s inner moons and exoplanets of Kepler-223

Three of Saturn’s moons — Tethys, Enceladus and Mimas — as seen from NASA’s Cassini spacecraft [image credit: NASA/JPL]

This is a comparison of the orbital patterns of Saturn’s four inner moons with the four exoplanets of the Kepler-223 system. Similarities pose interesting questions for planetary theorists.

The first four of Saturn’s seven major moons – known as the inner large moons – are Mimas, Enceladus, Tethys and Dione (Mi,En,Te and Di).

The star Kepler-223 has four known planets:
b, c, d, and e.

When comparing their orbital periods, there are obvious resonances (% accuracy shown):
Saturn: 2 Mi = 1 Te (> 99.84%) and 2 En = 1 Di (> 99.87%)
K-223: 2 c = 1 e (>99.87%) and 2 b = 1 d (> 99.86%)

Kepler-223 has another resonance: 2 d = 3 c (> 99.88%)
That means 8 b = 6 c = 4 d = 3 e (orbits)

The equivalent Saturnian moon numbers are: 32 Mi = 22 En = 16 Te = 11 Di
(For the moons to match K-223 exactly, the orbit numbers would have to be 32,24,16 and 12)

Turning to the syzygies, we can create charts to show the patterns:

Saturn chart
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The first three moons have the synodic ratio (yellow underlines):
6 Te-En = 10 En-Mi = 16 Mi-Te which is a 3:5:8 ratio (3,5 and 8 are Fibonacci numbers).
Accuracy 99.05 – 99.75%

Kepler-223 chart
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The planets c,d, and e have the synodic ratio (yellow underlines):
1 d-e = 2 c-d = 3 c-e (1,2 and 3 are Fibonacci numbers).
Accuracy 99.71 – 99.81%

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September 1, 2018 at 08:40AM