Elementary differential properties of the earth's gravity field

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Reilly, W.I. 1980 Elementary differential properties of the earth's gravity field. [s.l.]: [s.n.]. Report / Geophysics Division 162 63 p

Abstract: The differential geometry of the earth's gravity field is considered in terms of the variation of the orthonormal triad of unit vectors (lambdar, mur, nur) in the astronomical east, north and zenith directions, as related to a fixed geocentric triad (Ar, Br, Cr) by the astronomical latitude phi and longitude omega. Taking the astronomic longitude omega, latitude phi, and gravity potential W as a set of natural geodetic coordinates, the parameters describing the differential geometry of the gravity field are introduced as the components of the gradient vectors of (omega, phi, W) in the (lambdar, mur, nur) system. Expressions are developed in terms of these parameters for the rates of change of azimuth and zenith distance, of latitude and longitude, and of gravity potential and the intensity of gravity along observation lines in space. (auth)