ABSTRACT
Geometrical geodesy is the branch of science that deals with the Earth’s size and shape. Viewed from a large distance, the Earth appears to be nearly spherical, and, by comparison, the Earth is smoother than an orange-even when counting the highest mountains. If our planet Earth were reduced to a globe having a diameter of 1.0000 meter at the equator, the length of the spin axis would be 0.99665 meters, only 3.35 millimeters less. As postulated by Newton, this flattening at the poles is due primarily to the Earth spinning on its axis. The sea-level shape of the Earth is a continuous surface called the geoid. As such, it could be viewed as the surface of the ocean at rest (no tides) and extending coast to coast in a large transcontinental canal. An ellipse rotated about its minor axis-giving a three-dimensional mathematical surface called the ellipsoid-approximates this geoid shape of the world. The distance between the ellipsoid and geoid is called geoid height and varies, plus or minus, up to about 100 meters worldwide. Figure 6.1 is a meridian section of the Earth showing the poles, the equator, the spin axis, the mathematical ellipsoid, the geoid, the normal, and the vertical. Note that the ellipsoid-geoid separation and the Earth’s flattening are both exaggerated in Figure 6.1.
