I’ll bet a bottle of port that you were like me and thousands of others were entranced decades ago by the possibility of BCE longitude determination as brought forward by Hapgood's Maps of the Ancient Sea Kings. Years later, but still years ago, studying human migration theories and mitochondrial DNA distribution in the Americas led me (however circuitously) to question the possibility that the knowledge of precession (and the corresponding observations of precision) may have had not only a common knowledge/technology root, but perhaps more importantly have been a common cultural/economically driven pinnacle of achieved by Mediterranean (Greek/Egyptian/Babylonian), South American (Mayan) and Chinese cultures BCE, and if not BCE then certainly before the European Renaissance.

It was with this premise in mind that I came to hypothesize a means of longitude determination compatible with my understanding of BCE technology. Having been before the days of the web and knowing no one who could see why anyone would care, I left it on the shelf until reading Menzies 1421 and Marchants's Decoding the Heavens, interspersed with works of Joseph Needham (Heavenly Clockwork, Science and Civilization in China), Martin Isler (Sticks, Stones, & shadows), Nick Kanas (Star Maps), Kelly & Milone (Exploring Ancient Skies), and many others.

I propose for your critique that ancient cartographer/astronomers could have established approximate longitude +-10 degrees (yes that is not real impressive, and perhaps that is the same magnitude of limitation you point out in your post, but I am talking BCE) along with the much easier to determine latitude and charted the Earth before the Common Era with no more than a level, plum bob, clepsydra, gnomon, a solar-noon determined N/S line, and a star chart compiled at a "prime meridian" observatory. More important and what differentiates my hypothesis from others is what is not needed: observations or positions of any planet or moon, knowledge of planetary motion, telescope, units of time smaller than half a day, or math beyond simple addition and subtraction.

First some context:

Solar-noon is well documented in many ancient cultures as the means of establishing highly accurate (even in modern terms) north-south orientation, equinoxes, and solstices. Then just as today, noon was considered midpoint in a "day". For thousands of years before the Greenwich Prime Meridian was established (~1675) and subsequently Greenwich Mean Time along with time zones (1850s), communities calibrated their clocks to solar-noon. With the advent of time zones, wristwatches and GPS, solar-time has gone the way of the crystal radio. Like the crystal radio, solar-time lay within the modern premise, but is likewise lost in abstraction. The human abstraction of time being essential to my hypothesis it is important to note that GMT was created to mitigate the fact that for every step you take east or west you will have (however small) a different measurement for solar-noon. We observe solar-noon (and for that matter any moment of daily time) sweeping west from meridian to meridian at a rate of 15 arc-minutes for every minute of time, which equals one degree for every four minutes of time. At the equator that is roughly 900 nautical miles per hour.

Solar-midnight, on the other hand, is not well documented in ancient writings other than for its mystery, indeterminate nature and as being the transition point between days, the opposite of noon, and the middle of the night. It is for these very reasons that I suspect ancient astronomers would have had interest in investigating midnight and the stars that lay where the sun had been at mid-day before. Further, our ancient astronomer's time keeping technology, the clepsydra, would have easily determined the moment of midnight with a precision of seconds.

Geometrically speaking solar-time is defined by a plane established by a line crossing thru the Earth's north and south poles and the apparent center of the sun. This plane sweeps the universe once per solar year. The Earth rotates thru the solar-time plane once per solar-day and correspondingly 365.24 times per solar-year. Tangent to the surface of the Earth on the sunward side is solar-noon and on the umbra side is solar-midnight. The part we are most interested with here is the plane of solar-midnight that sweeps the universe once each solar-year which equals .98 degrees (roughly two moon diameters) per solar day. Again, each rotation of the Earth corresponds to the plane of midnight sweeping the universe by .98 degrees. It is as if three hundred sixty five (and a quarter) very tall and skinny Mercator projected maps of earth, each .98 degrees wide and 180 degrees tall (pole to pole) have been rolled out across the epileptic and at exactly solar midnight, the spot directly over your head precisely correlates to your location on the surface of the earth.

Now application:

The prime meridian observatory would have been elevated above its surroundings, topped with a gnomon (horizontal in the case of the renowned Dengfeng Observatory) and equipped with a clepsydra. To the north (south for southern hemispheric observatory) would be an area precisely aligned N/S and laid out for observing and tracking the gnomon's shadow from sunrise to sunset with the greatest possible precision. Each day the astronomers using their clepsydra would predict the moment of solar noon, and then confirm by shadow measurements the moment of solar noon, and read and record the actual measured duration of the last day. Armed with the duration of the previous day the astronomer can then predict the moment of midnight at which time the astronomer would sight along the N/S line. Imagine two parallel N/S lines of silk thread illuminated with a wax or oil pottery slit lantern, to keep the observer perfectly aligned thus inscribing a precise meridian line thru the sky, which would be recorded by the astronomer. As we think about it, it seems obvious that while the astronomer was at it, they would likely note yesterdays meridian now .98 degrees (=~1 degree = two moon diameters) to the west, and tomorrows meridian a likewise one degree to the east. Thus working ahead, and confirming behind, and making up for nights when the stars were occluded by weather. This can be simply replicated with modern astronomy software, but first you must compute accurate solar midnight for your longitude by hand, which is a pain because solar-midnight is not simply solar noon + 12hrs.

These meridians, one for each night of the year, will be useful for several years (with yearly 15.16176 arc-minute adjustments for the "extra" yearly quarter rotation and precession). Charts on brass or wood with rings or slides for yearly adjustments would have much greater longevity but no greater precision.

To be clear, I am not suggesting that our ancient mariner could just jump off a ship, eyeball N/S, count drops of water to midnight, look at a star chart and expect to figure out where he was. To the contrary, establishing best longitude required an investment of weeks or months and by this method could not possibly do so from the deck of a ship BCE.

Exploratory mariners setting out to sea would always want the latest meridian star chart. When upon uncharted shores, their cartographer/astronomers would focus their efforts on establishing an observatory as best they could (given available time, materials and environmental conditions) to build an observatory commensurate with the one back home. Important to recognize here are three critical resolution limiting factors:
1. Determination of N/S: winter months offers the greatest potential precision. Proximity to equator diminishes precision. Each arc-minute of N/S error imparts 6 degrees of longitudinal determination error.
2. Calibration of the clepsydra used for determination of solar-midnight: It seems obvious the sophistication, maintenance and tuning of the clepsydra requires talent, time and suitable environmental conditions for its operation. Each second of chronologic error imparts ~.5 arc-minutes of longitudinal error.
3. Precision of their determination of the N/S meridian bisecting the elliptic. Each arc-minute of error (1/30 diameter of moon) imparts 6 degrees of longitudinal error. Obviously one must be able to see stars that have been charted and do so via sighting mechanisms/structures that enhance precision.

The explorer with paper or parchment star charts would also need a "rule" of some sort mated to the map with gradients of 15.16 arc-minutes (likely a single unit of measure in their time) to compensate for the Earth's yearly extra ¼ rotation and precession. They would align their rule such that the .98 degree section was over the observed meridian. Then they would align the gradient of the current year with the nearest prime meridian (remember there is a prime meridian in the sky every .98 degrees in this system) marked by the astronomers back home. Then the longitude is indicated by where tonight's meridian crosses the ruler for "this year". So if this ruler was (for example) good for four years, then there would be four 15.16 arc-minutes measures followed by one .98 degree measure within which would indicate the local longitude.

This edit control says I am out of bytes....

What do you think Icosahedron?

Greenman (aka David Lee Cunningham)