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    Re: Longitude by altitudes. was Re: How Many Chronometers?
    From: Frank Reed
    Date: 2009 May 13, 06:39 -0700

    Marcel, you wrote:
    "Assuming that "they" (or your Romans) new:
    - how to calculate for a given day the position of the moon relative
    to the sun for e.g. the moment of sunset at their reference location
    (Rome, Babylon, Greenwich or whatever)."
    Well, we know what they knew (at least from c.200BC forward). They could 
    predict the Moon's position relative to the Sun to roughly ten minutes of 
    arc. A ten minute of arc error in the Moon's position corresponds to about 20 
    minutes of error in time, and those 20 minutes correspond to about five 
    degrees in longitude. So, yes, if you could take those predictions and then 
    compare them with the Moon's position in the sky (making the necessary 
    correction for the Moon's parallax) you could do some very general mapping 
    that way, with a very large amount of effort and central-planning. Would it 
    be any better than simply recording your course and distance run as you work 
    down a coastline? Probably not much better, if at all.
    "- how to measure latitude
    - how different latitudes shift the moment of sunrise/sunset
    - measuring shorter time intervals e.g. with a water-glass"
    I'm not sure where you're going here. Yes, the time of sunset at a known 
    latitude gives you the local apparent time. But then what? Where does the 
    water-glass come in?
    "It seems to me that with those preconditions it should have been
    possible to obtain at e.g. sunset the time difference between the moon
    positions of their reference location and the observed one and from
    this the difference in longitude."
    What do you mean by time difference? Let's say the crescent moon is in the 
    sky. If the Moon's horns are more or less horizontal, and I measure its 
    altitude, I can determine (after some fairly involved math) the absolute 
    time. To get longitude, we need to compare that with local time. And yes, 
    sunset can give you local time. So, we're back to my first comments to you on 
    this: to make all of this work, we need an algorithm for calculating the 
    Moon's position (or an observatory back home keeping fairly continuous 
    records of its position), and we need a portable instrument for making fairly 
    accurate measurements of the Moon's altitude. 
    If you want to postulate that they, whoever they were, invented the sextant 
    and created tables of the Moon's position comparable to those available in 
    the 18th century, and then all of that knowledge was lost, then yes this 
    works. But how is that history? There are surely ancient technologies that 
    were lost, as evidenced by the Antikythera device, for example. But even that 
    fascinating mechanical orrery does not contain any of the pieces necessary to 
    make this work.
    You concluded:
    "the moment of sunset should about be as accurate as the determination of the latitude."
    Sure. And that gives you local apparent time. You can also get local apparent 
    time by measuring the height of the Sun at any time, or you could do it by 
    carefully noting the stars in the zenith which simultaneously gives you 
    latitude (the method I described previously). Just bear in mind that to get 
    longitude we also need some absolute time or some signal that can be seen 
    everywhere on Earth (or at least a hemisphere of it) simultaneously. A lunar 
    eclipse could provide this very easily. A lunar altitude or a lunar distance 
    could also give you absolute time, but this is much more difficult (and also 
    more accurate).
    On a general note, why do people make maps? When Europeans developed 
    scientific mapping technologies, the first thing they did was map their own 
    countries, partly for science and partly for the vanity of the ruling class 
    (to see what they owned and controlled with greater realism). If there were 
    sophisticated mapping technologies in the Ancient Near East, I would expect 
    no less from them. Where are the detailed maps of Mesopotamia showing the 
    exact positions of the rivers, or maps showing the exact longitudes of the 
    great islands of the Mediterranean? Those surely would have been the first 
    targets for any such mapmakers. Unless these maps were made for religious or 
    spiritual purposes, practical charts of nearby lands would have been the 
    highest priority.
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