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In classical times (let's say 200 BC to 400 AD), how accurately could a Greek/Roman/Babylonian/etc. astronomer determine their location on the earth by coordinates like latitude/longitude?

Could they find their position to the nearest degree? Minute? Second?

I'm guessing they could find their latitude fairly accurately, but not have a good way of determining their longitude -- but I'm really not sure.

Note: This doesn't have to be at sea, it could be determining the position of a site on land. And I'm looking for how accurately they could determine latitude/longitude, not simply whether they could.

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Well, if they couldn't determine it, then I would say the accuracy is roughly zero. –  American Luke Jul 9 '12 at 22:41
    
@Luke, I'd have to agree with that. –  Joe Jul 9 '12 at 22:48
    
@Joe, I don't have enough info to compose a full answer but I'd like to bring up the case of Pytheas who is unfortunately known to us only by second hand relations (as is Himilco). One of the most interesting references on Pytheas is Barry Cunliffe's book (0140297847) and there is a fairly detailed discussion of latitude determination - and some evaluation of its precision - in wikipedia's article here‌​. –  Alain Pannetier Jul 11 '12 at 8:52
    
Some information about ancient latitude/longitude navigation system is in the 1421 book by Gavin Menzies. However, information in this book is certainly to be taken with caution, and I do not have my copy offhand. –  Jean-Christophe Dubacq Jul 13 '12 at 19:17
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3 Answers

Latitude can be calculated from observations of stellar objects (typically using something like an astrolabe) and a bit of math. The Greeks could do this as early as 150BC, but only on dry land. The Mariner's Astrolabe wasn't invented until around 1300 CE.

Nobody had a good way to determinte longitude in realtime aboard a ship before the invention of the marine chronometer in the early 1700's. The closest anyone came was the Chinese, who managed to work out the longitude of various places on the Indian trade routes in 1421 by placing observers on said places to observe various lunar and stellar positions simultaniously. This information may have made their maps better, but wasn't particularly useful to a navigator out of sight of land.

Before that, the typical technique used was dead reckoning, which was incredibly inaccurate. Basically, the navigator would chuck a hunk of wood out the back of the ship, try to estimate their speed based on their relative speed to the jetsam, and try to calculate their distance from the last time they did that based on that speed. Obviously this doesn't take currents into account at all, and any errors are likely to accumulate every time you do it.

What was typically done in the Medeteranian in ancient times was that navigators just kept themselves in sight of land. Even then, bad things could happen. For instance, the Odyssey is essentially a story of an ancient Greek who got blown off course sailing home from nearby Anatolia, and spent 10 years trying to find his way home.

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I'm aware of how you calculate latitude, but what I'm looking for is the accuracy. How accurately could the Greeks determine their latitude? –  Joe Jul 9 '12 at 22:19
    
I don't think it was possible to get accurate readings if they believed the Earth flat. Also, did they have the concept of this system, anyway? –  slybloty Jul 10 '12 at 13:22
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@slybloty - That's kind of a myth. The ancient Greeks realized the earth was spherical (and came up with a pretty good estimate of its size), and any mariner could look at the curved horizon and see it with their own eyes. –  T.E.D. Jul 10 '12 at 13:27
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@T.E.D. You might know that the earliest known Greek traveler to the English Isles is supposed to be Pytheas (it is as you may know the etymology of Britain, which suggests that Celts were probably as tattooed as the Picts themselves). Pytheas seems to have gone much further Northwards than Britain actually, was apparently enrolled for his mathematics skills and, more to the point - that was around 330/300 BC - had developed several ways to calculate latitude. Regarding the hunk of wood: that's the etymology of our... –  Alain Pannetier Jul 10 '12 at 21:30
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... log file ;-) –  Alain Pannetier Jul 10 '12 at 21:30
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The Greek astronomers (e.g. Ptolemy) could calculate longitude and latitude using spherical trigonometry. Their calculations are accurate on the assumption that the Earth is a perfect sphere. Our astronomers today believe that the Earth is slightly pear-shaped and consequently arrive at a slightly different calculation of longitude and latitude.

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PS, and of course the Greeks did not think the Earth is flat. –  fdb Mar 28 at 21:47
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References please re longitude. Being capable of measuring the Earth's circumference (as Eratosthenes did) is a far cry from calculating longitude. –  Pieter Geerkens Mar 28 at 23:12
    
The pear-shape of the earth isn't very relevant to ocean navigation, as it is in feet relative to thousands of miles. Latitude is easy, longitude, not so much. –  Oldcat Mar 29 at 0:41
    
@fdb At the risk of sound pedantic, whether or not the average Greek knew the Earth was not flat depends on the time period in question. Virtually all of the pre-Socratics believed in a flat-Earth cosmology. –  David H Mar 29 at 4:08
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First, a spot of background science. The Longitude Problem is exactly identical to the problem of establishing simultaneity on widely separated locations on the Earth's surface, and both prerequisite the existence of a reliable estimate of the Earth's diameter. Certainly Eratosthenes calculated the Earth's diameter in the 3rd Century BC, and other civilizations may have done so by roughly the same time period. However the problem of establishing simultaneity is more difficult, and comes in two flavours.

Longitude is calculated by comparing the elevation of an astronomical object to the pre-calculated (or observed) elevation of the same object at a reference location at the precisely simultaneous moment in time. Everything in the sky rotates once around that vast celestial sphere every 24 hours, so the more precisely one can establish simultaneity the more precise one's measurement of longitude will be.

The problem is simpler when the goal is cartography - calculating the longitude, and thus precise location, of a given spot on the globe exactly once. In this case one can use the occurrence of a predicted astronomical event as the definition of simultaneity. Surveying teams are organized to travel to the specified locales well in advance of the event, and providing the skies are clear on the given day the necessary observations are made. Once the surveying teams return the results are tabulated and the maps drawn.

The more difficult problem, and the one that confounded the British Admiralty into establishing the Longitude Prize, is of establishing the location of a moving vessel out of sight of land at whatever time the skies happened to be clear, wherever and whenever that was. One could not halt a sailing vessel in the middle of the ocean and wait for a pre-calculated event that occurred once or twice a month at best. It was necessary to resort to Dead Reckoning, a well-established and remarkably accurate science by the 17th and 18th centuries, which provided locations within one or two dozen miles on voyages thousands of miles long. When the goal was simply to voyage out and return home, this was more than adequate. However when the need is to avoid reefs of only a few hundred yards extent, being off by a few miles all too often results in foundering instead of sailing safely by.

The accuracy of dead reckoning can be judged by the quality of 16th and 17th century maps, reproductions of which are readily available all over the web. Don't be misled by the contours of western North America - those are due to the wanderings of the North Geomagnetic Pole.

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