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    Re: Sight Reduction method accuracy
    From: George Huxtable
    Date: 2004 Apr 5, 09:59 +0100

    Michael Boersma asked-
    >What is the difference between using the time of the meridian transit of
    >the moon to find longitude and using the lunar distance method of
    >determining GMT, thus longitude? The information for determining
    >meridian transit is on the daily page of the Nautical almanac as are the
    >tables for determining longitude from MT of the moon. Are these methods
    Would Michael please explain a bit further what he is after here? Does he
    assume that he has a chronometer on board, set to GMT? Or not?
    Even if he has, it would be a tricky business deriving a longitude from the
    chronometer-time of the Moon's meridian passage.
    Consider first his references to the Nautical Almanac. For each day, an box
    shows Moon meridian passage at Greenwich, but only to the nearest minute of
    time (= 15 arc-minutes of hour-angle). The other table Michael refers to
    (which is on page xxx11) is just an interpolation table allowing for
    adjustment of the time of Moon meridian passage at various longitudes, to
    cope with the wildly varying speeds of the Moon across the sky. Again, it's
    only in minutes of time, and in many cases the steps between table-entries
    are several minutes apart. It's not intended for navigational use, I
    presume. For any sort of navigation using the Moon, discard that
    information, and go by the hourly tables of Moon dec and GHA, given to a
    tenth-of-a-minute in each case.
    Even so, it isn't a simple business establishing the moment of meridian
    passage of the Moon, the instant when the Moon's GHA is the same as the
    ship's Westerly longitude. For the simpler case of the Sun, we have
    discussed, at some length, the difficulties in timing the moment of maximum
    altitude at that moment of apparent noon, and the resulting need to take
    equal altitudes equally spaced well before and well after apparent noon to
    achieve any real precision. We have also stressed the importance of
    allowing for the North-South component of the vessel's speed and the
    changing Sun declination. The same problems occur with the Moon, but in
    that case, the Moon declination can change at a rate of 40 minutes per
    hour, sometimes even more, giving rise to a BIG time-gap between the moment
    of meridian passage and the moment of maximum altitude.
    The above was just an account of the difficulties facing anyone trying to
    determine his longitude using Moon meridian passage, even if he knows his
    GMT from a chronometer.
    Without a chronometer, everything gets many times more difficult. Now, GMT
    has to be deduced from the position of the Moon in the sky, in relation to
    other bodies such as stars or Sun. Now, an error of 1 arc-minute in the
    Moon's position in the sky will give rise to an error of 2 minutes in GMT
    (on average), and therefore 30 arc-minutes of longitude. So everything has
    to subordinated to observing the Moon's position relative to the other
    bodies to the greatest possible accuracy.
    The biggest source of error in any sextant altitude measurement usually
    relates to uncertainties in the horizon. The lunar-distance method
    maximises its accuracy by making a direct angular measurement, across the
    sky, between the Moon and some other object which lies near its path. Even
    though it involves some contortions for the observer and his sextant, it
    avoids any use of the horizon as reference, and also avoids all the
    difficulties in timing Moon meridian passage that Michael's proposal would
    That measurement across the sky is about as simple and direct as it's
    possible to get, even if the subsequent corrections become rather
    complicated. Even so, because of that 30x lever-arm multiplying the errors,
    lunar distances can never achieve real precision at sea.
    Even a proficient navigator would not trust his deduced longitudes to be
    better than 30 arc-minutes from his true position.
    I hope this has answered Micheal's question, but if I have misunderstood
    something perhaps he will explain further.
    PS. Every time Michael Boersma posts a message, I recieve an attachment
    detailing his professional accomplishments, in the form of a "vcf card".
    Presumably, other listmembers receive the same thing, and we all have to
    delete it.
    The Nav-L list discourages (if not forbids) attachments, and I know that
    many users fear corruption from them (though my elderly Mac seems to be
    immune, which may be its only virtue). Some listmembers discard any message
    that carries an attachment, automatically.
    I have commented on this matter directly to Michael, off-list, but that has
    not stemmed the flow. Perhaps his email program sends the things without
    his knowledge.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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