CONSTRUCTION AND ACCURACY ESTIMATION OF DETERMINING THE EARTH'S GEOID BY ITS POTENTIAL

Authors

First and Last Name Academic degree E-mail Affiliation
Mykhailo Fys Sc.D. mykhailo.m.fys [at] lpnu.ua Lviv Polytechnic National University
Lviv, Ukraine
Department of cartography and geospatial modelling
Lviv, Ukraine
Andrii Brydun Ph.D. andrii.m.brydun [at] lpnu.ua Lviv Polytechnic National University
Lviv, Ukraine
Andrii Sohor Ph.D. andrii.r.sohor [at] lpnu.ua Lviv Polytechnic National University
Lviv , Ukraine
Mariana Yurkiv Ph.D. mariana.i.yurkiv [at] lpnu.ua Lviv Polytechnic National University
Lviv , Ukraine
Viktor Lozynskyi Ph.D. viktor.a.lozynskyi [at] lpnu.ua Lviv Polytechnic National University
Lviv , Ukraine

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First published on this website: 25.10.2020 - 10:46
Abstract 

The paper presents an algorithm for constructing a geoid based on the external gravitational field of the Earth, the radius vector of which is determined from the condition of the constancy of the potential on the equipotential surface. The values ​​of the coordinates of such a figure calculated by the iterative method are discrete points in space, and therefore, using them, it is possible to visually construct a three-dimensional geoid image or in the form of contour maps on a plane. A formula for an a priori estimate of the accuracy of determining the radius vector of the Earth's figure is derived, based on the theory of implicit functions of many variables. Approbation of the described technique is carried out on a specific example. The calculation results confirm the convergence of the iterative process in determining the values ​​of the radius vector and a high degree of calculation accuracy (5-6 cm). Therefore, this approach complements traditional assessment methods and can be fully used to study the shape of the Earth.

Keywords 
potential
References 
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Tue, 11/03/2020 - 21:44