
Actually, the importance of chronometers and accurate noon sights for navigation is vastly overrated. The more recent research indicates that until well into the 19th century, DED reckoning (for "deduced reckoning") was the preferred mode for most mariners. A good 15th-16th century navigator, for example, could hit a landfall after a trans-Atlantic voyage within 30-40 miles of his intended destination without ever taking a sight, simply by keeping track of his headings and his estimated speed through the water. Celestial navigation as we know it today (or did before GPS, at least) was a product of the need to nail down where specific pieces of land/territory were, not to figure out how to reach them. And the reason that was important was that Europeans were beginning to stake claims to other people's property all over the world and needed to be able to demonstrate conclusively which bit of property they were talking about. It didn't really supplant DED reckoning for maritime use until the age of flight, and even today a good sailor keeps a DED reckoning plot as a backup in case all the fancy electronics decide to hiccup and quit.
There are still at least a few of the "rutters," or sailing directions, composed by master mariners in the 16th century to allow for currents, wind drift, etc., which will allow you to sail from a point in the Med to one in South America without any instruments other than a compass and a way to accurately estimate your vessel's speed through the water. In fact, what made the Cahrisian merchant marine supreme on Safehold was the fact that there mariners had not only composed more of those "rutters" than anyone else but that the Royal College had collected and combined them more or les a la Nathaniel Bowditch.