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In this video is explained that in November 1584 the width of the Atlantic ocean was discovered by comparing the hour when the eclipse of the moon started in England with the hour when the eclipse occurred in Virginia USA. But doesn't also the Sun arise on particularly times in England and USA to calculate the distance? Why was the eclipse of the moon used?
See min 22:00 https://www.youtube.com/watch?v=w6JZSzVcKgo
Perhaps the following quotewill be more, ahem, illuminating.
As any Eclipse chaser can attest, total solar eclipses are extremely rare from any given location. A spot on Earth may go centuries before totality graces the skies. In theory, a partial would be much more common. And of course, this would require something such as smoked glass to observe first contact. That leaves us with lunar eclipses. Any given eclipse can easily span more than one full hemisphere of the Earth. Also, while contact with the diffuse outer cone of Earth’s shadow, or penumbra, is rather subtle, contact with the inner core, or umbra, is not. Such an event can be defined by eye to a span of time of about five minutes. Up until the time of the invention of the telescope, eclipse timing was the only semi reliable way to judge longitude. The idea is simple; observe the local time of first contact with the umbra, then compare it with the known time from a separate fixed location. The Earth rotates 15 degrees per hour, (360/24=15) or 1 degree every 4 minutes. If umbral contact was said to begin at 2:05AM at a given location and you observed it to begin at 1:05AM, you are 15 degrees west of the first location. The Greeks first noted this during an eclipse on September 20th, 331BC. Alexander the Great in Mesopotamia recorded the eclipse as beginning two hours after sunset, while on the north shores of Africa, the city of Carthage it was seen to start at sunset. Ptolemy correctly deduced that Alexander’s position was 30 degrees or 2 hours east of Carthage. None other than Christopher Columbus was a student of the works of Ptolmey. He attempted to use this method to judge his position on his second and third voyage to the new world. The eclipses concerned were on September 14th, 1494 (part of saros cycle #119) and February 29, 1504 (saros cycle #109).
Read the interesting book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time to find why measurement of longitude simply by observing the sun (or the stars) was impossible. Until there were accurate clocks.
More precisely, they tried to determine the difference of longitude between two places. The difference of longitude is the difference in local times at the places. While local time is easy to determine by astronomical observations, there is no simple way of comparing time at different locations. Moon eclipse is one such mean. The principle was clear from the antiquity, and this was the principal method of practical determining of difference in longitude between distant places, until the discovery of Jupiter satellites, which have two advantages: their eclipses occur more frequently, and also their eclipse times are easier to predict with high accuracy.
EDIT. One cannot use a Sun eclipse for this purpose. The difference is that Moon's eclipse occurs at a definite time, which can be predicted. So if one observer observes it at his local time $T_1$, and another at his local time $T_2$ then the difference of longitude it $T_1-T_2$.
Sun eclipses occur at times which depend on locations.
