Galileo researched the eclipses of the moons to a highly accurate degree - all with optics (designed a helmet / eyepiece too). Only problem was that it was a bit impractical on a pitching deck for longitude at sea…
Worked OK on land I think. All with mirrors / optics.
http://www.oceannavigator.com/May-June-2004/Longitude-by-Jove-navigating-with-Jupiters-moons/