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    Re: Use of Sun Sights for Local time, and Lunars for Longitude
    From: Bruce Stark
    Date: 2002 Oct 22, 13:09 EDT

    In your October 21 posting you say:
    >If you don't know how late it is at a particular
    >longitude, one way or another, i.e. if you don't know the phase angle
    between the
    >Earth and the sky, no magic is going to help you finding RA, hence LHA, and
    >of the Moon, both of which you need to compute its altitude. Local time at
    >unknown longitude is insufficient.
    If you have the local time you do in fact know how late it is at a particular
    longitude. You may not know exactly how far east or west that meridian is
    from Greenwich, but you know it's where you are.
    Moreover, local apparent time provides what I think you mean by "the phase
    angle between the Earth and the sky." It's the sun's hour angle, so if you
    have the latitude you can calculate the sun's altitude without further ado.
    DR longitude doesn't have to be close at all to give you an estimated GMT
    good enough for taking the sun's declination from the Almanac.
    Local time also tells you, well enough for most purposes, the local hour
    angle of the stars, since that changes only about 2.'5 per hour in relation
    to the sun, and declination is practically constant.
    The moon is another matter. She changes position in the sky, relative to the
    sun, about half a degree per hour. When you have to calculate her altitude
    you'd like to have Greenwich time within twelve minutes or so. But that only
    requires a DR correct to within three degrees.
    Now suppose you have the correct GMT and calculate the moon's altitude the
    modern way. That three degree error in longitude will give you a three degree
    error in the local hour angle of the moon, roughly thirty times the error
    you'd get with the old fashioned approach.
    As you've pointed out, LAT deteriorates quickly, partly because of slippage
    in the DR longitude. But, except in unfavorable weather, you corrected it in
    the morning or afternoon, a few hours before or after taking a lunar.
    Perhaps I shouldn't have used the word "flounder" in relation to "iteration."
    It's unnecessarily judgmental, and the only reason for my bias is the thought
    that someone turning to celestial navigation in a tight spot might not have a
    computer or electronic calculator at his or her fingertips.

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