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15 CHAPTER 2 GEODESY AND DATUMS IN NAVIGATION GEODESY, THE BASIS OF CARTOGRAPHY 200. Definition Geodesy is the science concerned with the exact posi- tioning of points on the surface of the earth. It also involves the study of variations of the earth’s gravity, the application of these variations to exact measurements on the earth, and the study of the exact size and shape of the earth. These fac- tors were unimportant to early navigators because of the relative inaccuracy of their methods. The precise accuracies of today’s navigation systems and the global nature of sat- ellite and other long-range positioning methods demand a more complete understanding of geodesy than has ever be- fore been required. 201. The Shape Of The Earth The irregular topographic surface is that upon which actual geodetic measurements are made. The measure- ments, however, are reduced to the geoid . Marine navigation measurements are made on the ocean surface which approximates the geoid. The geoid is a surface along which gravity is always equal and to which the direction of gravity is always perpen- dicular. The latter is particularly significant because optical instruments containing level devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The geoid is that surface to which the oceans would con- form over the entire earth if free to adjust to the combined effect of the earth’s mass attraction and the centrifugal force of the earth’s rotation. The ideal ocean surface would be free of ocean currents and salinity changes. Uneven distribution of the earth’s mass makes the geoidal surface irregular. The geoid refers to the actual size and shape of the earth, but such an irregular surface has serious limitations as a mathematical earth model because: • It has no complete mathematical expression. • Small variations in surface shape over time intro- duce small errors in measurement. • The irregularity of the surface would necessitate a prohibitive amount of computations. Figure 201. Geiod, ellipsoid, and topographic surface of the earth, and deflection of the vertical due to differences in mass.
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16 GEODESY AND DATUMS IN NAVIGATION The surface of the geoid, with some exceptions, tends to rise under mountains and to dip above ocean basins. For geodetic, mapping, and charting purposes, it is nec- essary to use a regular or geometric shape which closely approximates the shape of the geoid either on a local or glo- bal scale and which has a specific mathematical expression. This shape is called the ellipsoid . The separations of the geoid and ellipsoid are called geoidal heights , geoidal undulations , or geoidal separations .
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