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Alex E, you wrote:
"To estimate the accuracy, notice that the ratio
of the distance to the Moon to the Earth radius is
60 (very roughly). So the loss of precision due to the
method is by the factor of 60 under the most
favorable conditions."

It's 60 compared to observations made relative to a perfect terrestrial
horizon. Since a sea horizon has a typical inaccuracy of 0.5-1.0
minutes of arc from variable refraction, this method is only 6-12 times
less accurate than traditional celestial lines of position. It's just a
question of whether that's interesting or not (I won't suggest the word
"practical" in this discussion). Is there ever a case where it might be
interesting to get your position by celestial navigation to +/- 6
nautical miles when the horizon is not visible? To me, yes. To the next
guy in line, maybe not.

And you wrote:
"These most favorable conditions are:
a) The Moon is near zenith, and
b) The two directions Moon-star are perpendicular."

Yes, it's important for the Moon to be "well up" in the sky. If it's
not, the cones of position intersect the Earth at an oblique angle. The
more perpendicular, the better. And of course, with anything
"lunarian", it has to be that part of the month when the Moon is easily
observed.

Just so we're clear, unless I'm missing something, your point "b" is
nothing more than the usual condition for lines of position: you get
better results when the lines of position have a significant angle
between them. This is not a difficult condition if it's the middle of
the night. You've got all the bright stars in the sky and hours
available for taking sights -- no worries about the duration of
twilight.

"Now it is hard for me to believe that one can
measure distances with 0.1 or even 0.2 accuracy
permanently and reliably"

Sure you can! :-)
I have seen amateurs get 0.1 minute accuracy in lunars on the very
first try. It's about the sextant more than anything else. Myself, I
find a typical error of 0.2 minutes of arc, and if I shoot four and
average them, that yields 0.1 minutes of arc accuracy, again and again.
Of course, every once in a while my eyes will water or my hands will
shake, and then it's as much as ten times worse.

"I still have no definite opinion on this matter,
but my analysis of observations of Cook's expedition
seems to indicate much lower accuracy than 0.2'
And this was done from the ground,
by professional astronomers, possibly with the best
sextants ever made (?)"

It sure doesn't take a professional astronomer to use a sextant, though
in Cook's day I do agree that it helped! Of course, in Cook's era the
lunar distances in the Nautical Almanac had large intrinsic errors, so
even perfect observations could yield longitudes that were in error by
30 minutes of arc.

Anyway, my previous example was based on hypothetical observations (the
date of observation being five days in the future might have clued you
in on that ). Now that I have "discovered" this method or position
fixing, I'm gonna have to try some real observations. I'll see if I can
determine the location of Chicago from a downtown street corner without
any possibility of seeing a  horizon (within +/- 6 miles, that is).

-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars


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