Application of the Method of Models to the Analysis of Formulas for Determining the Figure of the Earth

摘要

Since, under practical conditions, the distribution of anomalies throughout the whole world is unknown, and gravimetric materials have many errors of gravity measurements and anomalies, four models were used for the evaluation of the errors of the formulas for determining the figue of the earth. The first model is a sphere with constant density, half immersed in a plane of infinite extension (without displacing its mass). The second model is a tore with heterogeneous density, half immersed in a sphere (without displacing its mass). The third model has also the form of a tore and sphere, but here the whole tore is situated within the sphere in order to satisfy the condition of Stokes' problem (lack of exterior masses). The first three models were used for the investigation of formulas based on Stokes' theory and the theory of studies of the geoid of a nonregularized earth. These models are inconvenient for the investigation of the formula determining the figure of the earth's physical surface, because of the discontinuity of the curvature of their exterior surface. Hence, a fourth model was used for the investigation of the latter formula. It had been obtained by the schematization of mount Alagez in Armenia (a cone with a flattened vertex set in a sphere). (Author)