[William Cloud Hicklin]

Remember that the Numenoreans and to a lesser extent the Gondorians were great mariners: which implies that astronomy was cultivated for the purpose of navigation. This might conceivably have even included longitude as well as latitude: there are clock-independent ways of calculating long, such as tracking Jupiter's moons, provided you have sufficiently accurate instruments and the tables worked out correctly. Nor I suppose should we discount the possibility that the Numenoreans had developed the marine chronometer, since even the backwards Shire-hobbits had clocks.