NavList:

Alex, you wrote:
"I can easily see them with my 8x40 binocular"

While true, it is important to say here that this visibility in binoculars has been a source of continuing confusion. Just seeing the Galilean moons of Jupiter is easy. They are regularly found at substantial angular distances from Jupiter, and they are bright. Were it not for the overwhelming brightness of Jupiter, they would be visible without optical aid, and we would probably count them as planets, by some definition.

But we cannot see the eclipses of the Galilean moons using binoculars!

You added:
"I sort of remember seeing an old nautical almanach which contained the tables for them."

Yes, certainly. This is largely a matter of long tradition, not evidence of practical value.

You wrote:
"One question is how accurately you can time an occultation."

In my own experience with 65x magnification using a 6"-aperture reflecting telescope on land in recent experiments, the eclipses can be timed to about 30-60 seconds. 

You suggested:
"But one could use satellite-Juiter distances instead. These can be surely measured by a sextant within 0'1 or 0'.2, and making tables for them is a routine matter."

This would serve no purpose. The angular distances of the Galilean satellites from Jupiter (or from each other) change much too slowly to serve any navigation purpose.

You asked:
"It seems that the method has better accuracy than Lunars, and requires almost no calculations. Was this method ever really used at sea? And if not, why exactly?"

It's impossible at sea because of the high magnification required to observe the eclipses. They occur quite close to the limb of Jupiter. They were available on land though the resulting time determination was only "comparable" to lunars, not better. And as Roger Sinnott has already mentioned, they could not be immediately compared with predicted eclipse times until the 20th century. In earlier centuries, it was necessary to compare observations in distant locations (e.g. Thailand) with similar observations (ideally with comparable telescopes) back home at some known longitude (e.g. Paris). Then the difference in longitude was simply the difference in local time, which also needed to be determined carefully to make all this work out. The resulting longitude difference might not be accurately known until months after the observations given the pace of "postal mail" traversing the globe in those centuries.

A few timing problems to keep in mind: 1) Like lunars, the Sun gets in the way. Galilean moon eclipses are not visible for a couple of months when Jupiter is behind the Sun, 2) Six months later, when Jupiter is near opposition, crossing the meridian around midnight, the planet's shadow is directly behind the planet blocking our view of eclipses, and 3) when you calculate eclipse frequencies based on Io's orbital period, remember that half occur in daylight on average even in the right seasons for the eclipses.

Frank Reed