Huh? Just how would that be done?
well ya see, Jupiter has nine moons, and depending upon how many of them you spot on a starry might, and who is in first place in the Eastern Division of the National league on August 15th, you subtract the sales tax, add the square root of your belt size, and turn left?
HHTH would I know this, Pabs? I am a trained sextant-and-tables-man. However, I know from my assiduous reading that certain highly skilled 18thC type navigator guys could do this. I also know from my own acute observations that you can actually see these little moon things flitting about Jupiter (and other planets) when you are out at sea and it's clear. Besides, everyone I sail with nowadays has GPS. I am usually good to 2 miles. They are good to 2 feet!
I also know that the Bumstead solar compass works ... just don't ask me how, OK? BTW, my admiration for old-time navigators increases all the time ... how these fellows actually got where they were going with their equipment is truly pretty darned amazing.
www.cosmicelk.net/Jupiter.htm
Seems you sort of use Jupiters Moons as your clock. Try this at home, just not at sea with me aboard.
At sea, on a clear night the moons of Jupiter can actually be seen with the naked eye. The fix apparently involved timing their passage across the face of the planet, checking the time, how many of the nine were visible, angles to other stars, and the clincher, going below and checking one's results against GPS (made in China and I made that up.)
BTW, Chinese sailing vessels may look and smell like junk, but those odd-looking things that I certainly wouldn't want to see tied up at my YC could evidently rapidly sail rings around the first Western ships to encounter them. Their sails look more like your Aunt Fanny's porch shades, but they do have the effect of being fully battened, very easily reefed, and are very aerodynamic. To give those oriental chaps their long overdue, they also invented the compass (reportedly), the centerboard, the lifting keel, water-tight compartments, and the transom-mounted or center-line rudder. Gave us round-eyed devils a whole new slant on sailing.
There is little doubt that the Chinese once explored the whole Pacific. However, this glimpse of the outside world apparently frightened their eunuch mandarin bureaucrats and the emperor, and all further exploration was stopped. That pretty much puts paid to the notion that the Incas were having their suits made in Hong Kong or the Aztecs sending their laundry to Shanghai.
Maybe those Italian yachtsmen were definitely NOT the first to see our continents, but they certainly put North, Central, and South America on the map, one of them modestly enough, naming the place after himself, or at least not correcting the mapmaker who did.