The Galilean Satellites are the 4 largest moons of Jupiter. They are Io, Europa, Ganymede and Callisto. This website has some basic information about the Galilean Satellites. http://en.wikipedia.org/wiki/Galilean_moon
The Golden Ratio is a transcendental number, which makes it an axiom or a self-evident starting point. The Golden Ratio in very evident in science, mathematics, nature and etc.
Let PHI be the Golden Ratio, which is 1.6180339887…
PHI = 1.6180339887…
phi = PHI – 1 = 0.6180339887…
Note: ‘^’ means ‘to the power of…’
The Galilean Satellites’ distance from Jupiter:
Io – 421000 kilometers
Europa – 670900 kilometers
Ganymede – 1070400 kilometers
Callisto – 1882700 kilometers
Europa / Io
= 670900 / 421600
= 1.5913
(PHI within 98.35% accuracy)
Ganymede / Io
= 1070400 / 421600
= 2.5389
(PHI^2 within 97.55% accuracy)
Callisto / Io
= 1882700 / 421600
= 4.4656
(PHI^3 + phi^3 within 99.85% accuracy)
Ganymede / Europa
= 1070400 / 670900
= 1.5955
(PHI within 98.61% accuracy)
Callisto / Europa
= 1882700 / 670900
= 2.8062
(PHI^2 + phi^3 within 98.32% accuracy)
Callisto / Ganymede
= 1882700 / 1070400
= 1.7589
(PHI + phi^4 within 99.71% accuracy)
This shows a very strong connection between PHI and the 4 largest satellites of Jupiter.