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    Re: Datum for Nautical Almanac
    From: Herbert Prinz
    Date: 2004 Oct 30, 14:05 -0400

    Charles Seitz wrote:
    
    > This, I assume means with respect to observations from a spherical earth.
    > But, we all know the real earth is better  modeled as a geoid.  That means
    > observations made with respect to the local horizon on the real earth will be
    > slightly
    > different than those made from a spherical earth.  It follows that circles of
    > equal
    > altitude, the basis of CN,  are not perfectly circular.
    
    Circles of equal altitude are perfectly circular if you draw them in the
    celestial sphere. You should not draw them on the surface of the earth.
    
    > (I suspect observations of altitude would be nearly identical for both
    > reference systems at the poles, equator and near 45 deg lat.  At these
    > locations, the center of the earth will be directly under you)
    
    Actually, at 45 deg latitude, the centre of the Earth is the farthest away from
    the local vertical.
    
    
    > Since there are numerous geodetic datams, your geographical position does
    > indeed depend on your assumed datum.  So, why wouldn't there also be
    > some inherent positional discrepancy between a geocentic and geoidal earth
    > model?
    
    Forget Geographical Position. Check the archive for my rant from 2002-01-21,
    "The Mischief of Geographical Position". It has the answer to your question.
    
    
    > I suspect that sight reduction tables would be nearly impossible to prepare
    > if all of the possible complications were considered.  We choose an earth
    > shape
    > model that works best for a particular purpose.
    
    The opinion that the shape of the Earth does not matter for celestial navigation
    because the sphere is good enough an approximation is very common, but totally
    wrong. At latitude 45 deg, the distance between geocentric and geodetic latitude
    is 12 nautical miles. Such a mistake will easily get you into the reefs at the
    approach of Bermuda. So, what is the real reason why the shape of the earth does
    not matter?
    
    When a celestial navigator speaks of his "position" he really is talking about
    the orientation of his sail mast (i.e. local vertical) with respect to the
    celestial sphere. Nothing else. He could not care less whether the line through
    the mast points to the centre of the Earth or not.
    
    When the chart maker speaks of the "position" of a lighthouse, he talks about
    the orientation of a plumb line at the place of the lighthouse. Until recently,
    he had no alternative method. This plumb line and the sail mast will coincide if
    and only if the boat is about to hit the lighthouse. That's why cel. nav. works
    independent of datum.
    
    GPS works differently in that it establishes 3-dimensional positions in
    Cartesian space. These can only be mapped to the surface of the Earth if the
    shape of that surface is known.
    
    
    Herbert Prinz
    
    
    

       
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