Determination of ellipsoidal corrections to quasi-geoid heights

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Space Geoinformatics and Geodesy
1Sohor, AR, 1Brydun, AM
1Lviv Polytechnic National University, Lviv, Ukraine
Space Sci. & Technol. 2026, 32 ;(1):76-81
https://doi.org/10.15407/knit2026.01.076
Publication Language: English
Abstract: 
The problem of studying the external gravitational field of the Earth is to examine the shape of the Earth. Such a problem is based on determining the theory of the potential of the Earth’s gravitational force. In studying the gravitational field and shape of the Earth, in particular, the method of expanding the potential into a series of spherical functions is used. This method of depicting the potential is quite convenient for studying the shape and gravitational field of the Earth from disturbances in the motion of artificial satellites of the Earth. This method makes it possible to depict the gravitational field, known on a spherical model of the Earth, as a sum of harmonics, and the higher the ordinal number of the harmonic, the shorter its wavelength. Specifying the coefficients of such a trigonometric series is quite convenient for various calculations. Research on determining the shape and dimensions of the Earth by the method of expanding the potential into a series of spherical functions was carried out in detail by famous scientists H. Moritz, D. Zagrebin, P. Dvulit, J. Neumann, B. Hoffmann-Wellenhof, V. Heiskanen, and D. Lelgemann. Spherical approximation is still used in physical geodesy. However, this is insufficient to obtain more accurate calculation results since modern gravimetric and altimetric satellite measurements give more precise results in an order of magnitude. To obtain more accurate calculation results based on modern gravimetric measurements, which will be commensurate with the data of modern satellite measurements (for example, obtained using Global Navigation Satellite Systems), it is necessary to take into account ellipsoidal corrections to the components of the Earth’s anomalous gravitational field. The article aims to determine the values of ellipsoidal corrections when calculating the heights of the quasi-geoid as one of the components of the Earth’s perturbing potential. To prove or disprove the feasibility of considering ellipsoidal corrections when calculating the heights of the quasi-geoid N by comparing their results with the accuracy of modern high-precision altimeter-gravimetric observations of the Earth’s anomalous gravitational field.
Keywords: altimeter-gravimetric calculations; anomalous gravitational field; the height of the quasi-geoid; ellipsoidal correction; spherical functions; global geocentric system; European regional geodetic system
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