It turns out that the Galilean satellite system around Jupiter can be considered as some kind of natural Cosmic Clock.

At the time of Galileo, the determination of longitude is a significant practical problem King Philip III of Spain offered a prize for a method to determine the longitude of a ship out of sight of land. Galileo proposed a method of establishing the time of day, and thus longitude, based on the times of the eclipses of the moons of Jupiter, in essence using the Jovian system as a cosmic clock.

Recall that the orbital period of IO is 1.85 days and there are essentially 4 "eclipses of IO per orbit. So eclipses of IO are frequent. However, a) its hard to accurately observe the eclipse on a rocking boat and b) Galileo's eclipse timetables weren't all that accurate.

Moving forward to 1666:

• Cassini (in Paris) observed around 200 eclipses between 1666 and 1668 and noticed that there were discrepancies between the actual eclipse and the predicted time of the eclipse.

• The only logical resolution to this was that the speed of light was finite so that the actual eclipse time depended on the distance between the Earth and Jupiter (which is continuously varying).

• Ole Romer made similar observations (near Copenhagen) and by comparing notes with Cassini, the difference in longtidude between Paris and Copenhagen (actually Uranienborg) was established.

• Romer estimates, from these timing discrepancies, that it takes 22 minutes for light to travel a distance equal to the diameter of the Earth's orbit. (so the distance between the Earth and the Sun is 11 light minutes). This leads to a velocity of light = 135,000 km/s (not the right answer but close enough to show its really, really, fast!). This is published in 1675.

  In 1809, again making use of observations of Io, but this time with the benefit of more than a century of increasingly precise observations, the astronomer Delambre reported the time for light to travel from the Sun to the Earth as 8 minutes and 12 seconds. Depending on the value assumed for the astronomical unit, this yields the speed of light as just a little more than 300,000 kilometres per second (the right answer).