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Figures 9a through 9d show, in cartoon form, the juxtaposition of two astro- geodetic datums with the geoid and a global datum. In figure 9a we see the geoid. There is an outline for representation in the other figures. In figure 9b red and green astro-geodetic datums are shown connected to the surface at two different points. The differences are exaggerated for effect. Figure 9c shows the geoid and the global datum. Figure 9d shows all three ellipsoids juxtaposed with the center of the ellipsoids clearly shown in three different places (again exaggerated for effect). Since latitude and longitude are referenced to the centre of the respective ellipsoid, it is clear that a latitude and longitude on one datum will not be compatible with a latitude and longitude on another datum unless some sort of transform takes place to adjust the one to match the other.
Reference Datum Transformation: Figure 10 shows a global (blue) and an astro-geodetic or regional datum (green), with the offset of the two centres. In order for a coordinate on the blue datum to be transformed to the green datum, the latitude and longitude have to be converted to x,y,z Cartesian coordinates on the blue datum. The dx, dy, dz have to be applied giving the x,y,z on the green datum. This can then be converted back to latitude and longitude on the green datum.
Figure 10: Showing a global datum (blue) and a regional/astro-geodetic datum (green) and the application of the geocentric transformation. The point P has not moved. It is just described by different coordinates.
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