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    Re: Sextant Positions versus Map Datums?
    From: UNK
    Date: 2002 Jan 17, 11:33 AM

    On Wed 16 Jan 2002 10:07 PM in Navigation-L,
    Trevor Kenchington [mailto:Gadus{at}ISTAR.CA] said:
    > As I understand it, the various datums are different ellipsoids,
    > each of which is a mathematically-perfect surface which closely
    > (but not perfectly) matches the shape of the real globe, the
    > early ellipsoids differing in which part of the real globe they
    > most closely matched. Surely then it is not the landmarks which
    > move (they, after all, are rooted on bedrock) but the positions
    > of latitude and longitude lines which are defined relative to
    > the particular ellipsoid?
    
    Actually, it is the landmarks that appear to "move" between charts
    with differing datums.
    
    Underlying each datum is an ellipsoid. The ellipsoid is an idealized
    smooth surface chosen to minimize differences between itself and
    the geoid (a theoretical earth with all points at "sea level" and
    with the surface everywhere perpendicular to the local gravity
    vector) for the area covered by the datum (North America for
    NAD-27) or worldwide (WGS-84).
    
    The equator is a plane through the center of the earth perpendicular
    to the axis of the poles. The prime meridian is a plane through the
    poles that passes through a selected point (Greenwich). The
    longitude of any other point is the angle between its meridian
    (plane through the poles) and the prime meridian. The latitude is
    similarly measured as the angle between the equatorial plane and
    its prime vertical, a plane through the point (and the center of
    the earth) and perpendicular to the point's meridian.
    
    The point to bear in mind is that lat and lon are angular measures
    between intersecting planes. Project these planes to the stars and
    you have celestial lat/lon, which, translated into declination and
    hour angle, is the basis for celestial navigation. A position
    calculated from celestial sights references these planes.
    
    Where these planes intersect the surface of the earth, or of an
    earth-size sphere or ellipsoid, you have the geographic lat/lon of
    a point. However, the difference between the lat/lon on the
    celestial sphere and the not-quite spherical earth is vertical.
    The planes and the angles between them remain the same. Only the
    distance from the center of the earth changes with the surface
    we've chosen.
    
    [Diagram of lat/lon planes intersecting concentric sphere and
    ellipsoid desperately needed here!]
    
    So what's the datum shift between charts?
    
    A plotting sheet for a given latitude gives you a place to plot
    a position by lat/lon, or by reference to some other point
    previously determined. A chart is a plotting sheet with landmarks
    (land, shoals, channels, etc.) already plotted for you. Plotted
    how?
    
    Each horizontal datum begins with a set of reference points whose
    lat/lon is determined as accurately as possible. From these
    reference points, ancient or modern surveying methods are used to
    assign latitude and longitude to other landmarks, and you have a chart.
    Newer datums have more accurately determined base references and
    more accurate surveys from them. But it's not the underlying
    latitude and longitude that shifts between datums, its the assignment
    of lat/lon to landmarks.
    
    Thus, if you take a lat/lon and plot it on charts with two different
    datums, it's still the same lat/lon on both, but the distance and
    bearing from that lat/lon to a given landmark may change. Likewise,
    a landmark, or a point determined by range and bearing from it may
    plot at different lat/lons on the two charts.
    
     -- Peter (where did my lunch time go?!)
    

       
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