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    Re: equal altitudes
    From: Bill Murdoch
    Date: 1997 Dec 04, 3:57 PM

    We have been back and forth over the last couple of weeks over using different
    methods of reducing sun sights.  It seems that no one objects to using a noon
    sun sight to determine latitude.  It is not hard to find the altitude where
    the sun stops rising, and the math is simple with the navigational triangle
    collapsed to a line.  You can reduct the sight with simple addition and
    subtraction.
    
    The rub comes with using the noon sight to find longitude.  It seems to me
    (and I have never done it anywhere but in my backyard) that if at noon the sun
    is passing somewhere near overhead it would work and if the sun is near the
    horizon it would be difficult at best.  With the sun passing overhead it will
    be rising at 15 deg/hr before noon and setting at 15 deg/hr after noon.  For
    only the shortest of instants would it not be moving.  That should be an easy
    spot to find.  Just take a sight while the azimuth is still east and another
    at the time the azimuth is west and the altitude is the same as the first
    sight.  Split the difference and you have the time of noon; a little
    arithmetic and you have the lngitude.  However, if the sun were near the
    horizon at noon, it would be rising very slowly in altitude before noon and
    setting in altitude very slowly after noon.  It would be hard to tell the time
    when it stopped rising and started setting.  In fact for someone near the pole
    for whom the sun neither rises nor sets it would be impossible to tell the
    time of noon and thus impossible to tell the longitude by this method.
    
    The use of sight reduction tables or a calculator to solve the navigation
    triangle as was pointed out gets around all of this, but books and trig scare
    most people to death.  To bad.  They miss a lot.
    
    That little calculator can do more.  It can not only replace the sight
    reduction tables; it can also replace the almanac.  Try the attached form.  It
    can be used to calculate the GHA of Aries.  Any trig calcualtor with one
    memory should work so long as it keeps 12 digits or more internally.  It is
    not hard to do the almanac calculations.  100 years ago they were all
    calculated by hand.
    
    (I hope the form is without mistakes.  I have not had time to exhaustively
    check it.  Let me know if you find something wrong.)
    

       
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