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    Re: Latitude by Lunar Distance
    From: Frank Reed CT
    Date: 2006 Oct 05, 20:01 -0700

    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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