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    Re: Lunar distances
    From: George Huxtable
    Date: 2002 Jan 28, 4:14 AM

    Eric Haberfellner writes-
    >I am not an expert on Lunars, but I believe that Lechter gives a complete
    >solution. He states:
    >"In discovering a way to solve it [GMT by lunar distance] using only the
    >Nautical Almanac and the ordinary sight reduction tables I had on board
    >(H.O. 214), I experienced one of the great intellectual triumphs of my life.
    >On the 25th day of the passage, with 500 miles to go, I was able to prove
    >beyond all doubt that my clock was correct, within one minute of GMT, so my
    >longitude was gound within 30 miles or so - ample precision for the upcoming
    >This was in 1963. Did the Nautical Almanac still have Lunar distance tables
    >at that time? I will have to dig into this material to figure out what
    >information he actually uses from the Nautical Almanac. I don't have time
    >right now.
    >He has some equations, and gives complete examples.
    >Eric Haberfellner
    In response to this message, here are some comments from George.
    The author of the book in question is named Letcher, not Lechter.
    In 1963, the Nautical Almanac did not contain Lunar Distance tables: nor
    had it for more than 50 years.
    I have some regard for Letcher, who wrote a really clear book on
    self-steering many years ago.
    I don't have a copy of his "Self-Contained Celestial Navigation with
    H.O.208" by John S. Letcher, Jr., published by International Marine
    Publishing Company in 1977. However, Bill Murdoch has kindly promised to
    send me relevant extracts.
    In advance of knowing exactly what Letcher says about the matter, it's a
    bit dangerous for me to pontificate about it. But I can say this with some
    It is, indeed, possible to use an altitude of the Moon as a normal position
    line, and to deduce the time without measuring a lunar distance. The snag
    is that measuring up from the horizon includes any unknowns in the dip of
    the horizon, and that can be the principal error in a sextant altitude. The
    lunar-distance method does not involve the horizon at all so it is capable
    of providing high precision in the hands of a skilled observer. Extreme
    precision in that angle measurement is vital because of the slow motion of
    the Moon against the rest of the sky background.
    However, I suggest that Letcher's statement, as quoted, "I was able to prove
    beyond all doubt that my clock was correct, within one minute of GMT"
    should be treated with some caution. It must presume that Letcher could
    somehow determine the Moon's position to within half a minute of arc, which
    (presumably) from a small boat, is good going indeed. "Prove beyond all
    doubt" seems to me to be overstating things a bit. When he goes on to claim
    that his longitude was good to 30 miles or so, that is getting more
    acceptable (depending on his latitude at the time).
    I look forward to reading the details of Letcher's claim, and perhaps it
    may even persuade me to revise that opinion.
    You may wish to follow up the question, first raised by Francis Chichester,
    about obtaining longitude from lunar altitudes, rather than from lunar
    distances. There is an authoritative paper on the subject from D H Sadler,
    then Director of HM Nautical Almanac Office. It's "Lunar Methods for
    'Longitude Without Time'" in Journal of Navigation (the British one, not
    the American) 31,2. May 1978, page 244. It has references to many earlier
    papers on the topic, but contains a rather inscrutable diagram which is
    quite beyond me.
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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