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    Re: Latitudes by lunar distance. was: Lunars with and without altitudes
    From: Dave Walden
    Date: 2006 Nov 26, 14:23 -0800

    Apologies for the lack of documentation in the code.  Like many/most
    engineers and scientists, I find the work fun, the report writing less
    so.  I realized that if I didn't "just send it", I'd probably
    move on and never come back to write it up more properly.  So again,
    apologies, and I'm more than happy to provide any
    answers/help/additional details people would find interesting.
    
    The previous post is a place to start on Maxima documentation.  A
    reference I find useful is Michael Clarkson, DOE-Maxima Reference
    Manual, ver5.9, Aug 2002.  (Try google for macref.pdf)
    
    %i10 is the usual equation for cleared lunar distance (Cotter p212
    bottom following "From which:") I actually took it, with the fairly
    widely used notation, from, "Josef de Mendoza y Rios", Recherches
    sur les principaux Problemes de l'Astronomie Nautique, p79, as
    discussed earlier.  In FORTRAN (and radians):
    
    D=acos(
    (cos(d)-sin(a)*sin(h))*(cos(A)(cos(H))/(cos(a)*cos(h))+sin(A)*sin(H))
    
    Where, D is cleared distance, d is observed, a is apparent moon
    altitude, A is true moon alt, h is apparent star/sun/planet altitude, H
    is apparent star alt.
    
    Using the Nautical Almanac algorithm for position from intercept and
    azimuth by calculation p282, I get W69-33, N38-40.  I purposely used
    Nautical Almanac precision.  I will repeat with ephemeris values.
    
    On SD, I may have mistakenly used 16.2 for one star and 16.1 for the
    other.  I meant 16.1.  This is the Nautical Almanac value.  It agrees
    to the nearest 0.1' for 30 to 60 degrees to the more precise value in
    this case.  Again, more precision is possible.
    
    On refraction, that is indeed the method I used.  I stopped at one term
    because it gave accuracy consistent with other choices.
    
    On parallax, yes the issue is the "backwards" correction.  See for
    example, John Brinkley, Elements of Astronomy, 1819, pg 319.   (Google
    books, full text)
    
    On earth shape, yes I neglected it for this calculation.  Could be
    easily added.
    
    Next topic, eliminate need for AP.  Approach, solve for equation of
    cone in space on which observed lunar distance is found.  Find
    intersection of cone with sphere (earth) ((or flattened sphere)).
    Repeat for second cone/star.  Intersection of two lines on sphere is
    position.  (Unless one or both stars are very close to the moon, there
    will only be one such intersection.)  I think I'm still a few days
    away.  Anyone done it?
    
    Sorry, what computer "basic" matter?
    
    
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