The new theory of the gravimetric geodesy (II)
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Date
1959-12
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University. Division of Geodetic Science
Abstract
According to Helmert, the function of geodesy is to measure and represent the physical surface of the earth, "Ausmessung und Abbildung der Erdoberfläche." This problem is practically solved in three steps. 1. Establishment of a reference surface which must be as regular as possible, but at the same time, sufficiently close to the actual surface, 2. Establishment of an intermediate surface and determination of the deviations of the latter from the reference surface, 3. Determination of the deviations of the actual surface from the intermediate surface. For the purposes of pure geodesy, the first step is definitely completed by the international ellipsoid. There is no need to replace the constants given on pp. 18-26, Part I, by values which would represent the actual earth more closely. As for step 2, the classical theory introduced the geoid as the intermediate surface. This is a smoothly undulating surface which runs close to the ellipsoid; the deviations, which are of order of 50 meters, can be determined with the aid of the famous formulas of Stokes. The distances involved in step 3 are long, often several kilometers. They are called orthometric heights. The increasing accuracy of the practical measurements has shown that the classical theory fails to satisfy the modern requirements of the precision. According to the old theory, the following reductions should be applied to the measurements: a. The results of spirit levellings should be converted to orthometric heights, b. The direction of the actual gravity as obtained with the aid of the astronomical fixations at the physical surface of the earth should be reduced to the geoid, c. Similarly, the values of gravity observed at the earth's surface should be reduced to the geoid. These reductions require such information about the circumstances within the earth's crust--as the gravity or the density of the matter-- which practically never can be obtained. Very good approximations can be computed with the aid of plausible hypotheses but, anyway, the computations often are very cumbersome. On the other hand, many investigators have shown that these hypotheses are quite unnecessary. No one, however, has clearly pointed out that the new methods of reduction signify the abandonment of the geoid as the intermediate surface, nor has anyone exactly defined the new intermediate surface. In this paper a comprehensive new theory will be developed on the basis of the ideas that have been presented by Stokes, Pizzetti, Somigliana, Vening Meinesz, Jeffreys, Molodensky, de Graff Hunter and many others. There will be only a few references in the text because the ideas mostly are generally known; the omission of the bibliographical sources, in most cases, is due to the fact that the author has not been sure of the origin of each idea. [Full text of abstract available in document.]
Description
Prepared for Air Force Cambridge Research Center, U.S. Air Research and Development Command, Laurence G. Hanscom Field, Bedford, Massachusetts: Contract No. AF 19(604)-1963 (OSURF Project 716)