# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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.

And:
"- 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?

And:
"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.

-FER

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