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Probably too late to help much, I have changed the thread title.

Marcel, you wrote:
"Regarding the logistics problem: Having seen on TV a "documentary" on
the various expeditions which were undertaken to observe the Venus/Sun
transits of 1761 and 1769 at various places of the earth let me
question whether their would have been much earlier an easy solution
to "think of a way around that"."

Right, but the whole idea that the Piri Reis map represents some ancient 
seafaring culture (worth considering, even if it's not likely) depends on 
some lost ability to sail great distances. One of the key technologies that 
enabled those voyages by Cook and others in the 18th century was just good 
diet. Scurvy was as much of a problem for those early northern European 
voyagers as uncertain longitude, maybe more so. Now imagine an ancient 
seafaring culture that has by chance avoided the problem of scurvy. Maybe 
they eat lots of oranges on a regular basis. Such a simple thing, not at all 
improbable, would have changed everyting. It is at least conceivable that 
they might have undertaken planned, intentional, long-distance voyages with 
some degree of success even three or four thousand years ago. So who knows... 
maybe that logistical problem is just a matter of funding! The Britain that 
sent Cook on his journeys was an impoverished place in many ways when 
compared to the ancient and classical civilizations of the Mediterranean. 

Anyway, back to NavList's main topic. How might they have navigated? And could 
they have used the Moon for longitude?

You wrote:
"If the Saros cycle was known, it could possibly also be used for predictive 
calculations such as for setting up a sort of ephemerides."

The Saros cycle was definitely known, and it is a remarkable testament to the 
state power that supported such studies millennia ago. While the Saros cycle 
helps a great deal, especially when predicting eclipses, it doesn't tell us 
anywhere near enough to be able to use the Moon's altitude for longitude. But 
predicting eclipses is certainly an "enabling technology" for the Ptolemaic 
plan of observing a lunar eclipse from scattered points around the globe. It 
could be done!

Yesterday or the day before, I posted something that was incorrect. I said 
that in the Roman period, they could predict the position of the Moon within 
ten minutes of arc. That was too generous for predictions by a factor of six 
or so. They could predict the Moon's position within a degree or so. Now 
since the Moon takes two hours to move a degree relative to the Sun and other 
celestial objects, a one degree error in the Moon's position means a two hour 
error in absolute time or a thirty degree error in longitude. So the 
available prediction algorithms would have been essentially useless for 
longitude. And yet even without a proper model of the Moon's motion, if we 
simply have an observatory --well-funded, well-staffed-- recording the Moon's 
position every hour of every day (while it's above the horizon naturally) 
then we can compare our position information with similar position 
information gathered at distant locations. And in that case, they could have 
probably counted on accuracies of about six to ten minutes of arc in the net 
comparison, which corresponds to 3 to 5 degrees error in longitude, and that 
wouldn't be entirely useless.

You wrote:
"if we haven't found such a document doesn't mean that it didn't exist."

Without a doubt. I would say that it's considered "canonical" that huge 
quantities of astronomical documents existed two thousand years ago which 
have now been lost. We need a time machine and a library card to the library 
at Alexandria. They're in there, for sure. :-)

And:
"Don't misunderstand me. I don't want to "proof" here something. It just was 
an effort to sketch how a possible method might have been for measuring 
longitude without the means which became available later."

Yes, I understand you. No problem.

Neither the lunar distance method for finding longitude nor the method of 
finding longitude by lunar altitudes (closely allied) required any great leap 
in science to understand. The concept is simple enough, and Ptolemy et al. 
would surely have recognized it as an extension of the eclipse method. 
There's no "rocket science" in it. But again, it all hinges on tables of the 
Moon's position much more accurate than those known to have existed, OR it 
requires one or more serious observatories making continuous observations of 
the Moon's position, and it requires an instrument like the modern sextant. 
These things could have existed and been washed away. That's certainly 
possible. From my perspective, if they did exist, I would expect more 
evidence of their existence... not just a single map with a vague coastline 
of South America, but other accurate maps of points with much greater 
importance nearer to home, wherever that might have been.

-FER




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