Purpose. Planetary problems play in geosciences very important role. The aim of this work is to improve methods and algorithms for approximating of the physical surface of the planet by biaxial and triaxial ellipsoid for study the dynamics of change of its shape. Methods. Classical approaches to the determination of Earths shape provide computation of evolution ellipsoid parameters of that in the best way fits to geoid, or quasigeoid. Such approach allows to provide initial reference surface for many coordinates systems. The problem of determination of the size and orientation of the ellipsoid that most closely matched to the surface of the Earth's lithosphere is very relevant for the study of geodynamic processes in a planetary scale. The solution to this problem is considered on the example of lithosphere heights approximation by biaxial and triaxial ellipsoid. Described in paper algorithms was used to for the approximation of the geoid model EGM2008 and DEM ETOPO1. For the approximation we used average values of geoidal ondulation and physical surface heights within 5º×5º spherical trapezoids. To verify algorithm we compare approximation result obtained by the proposed methods. Results. Comparative analysis of obtained results indicates that proposed approximation methods are reliable and can be used for the investigation of Earths planetary dynamic. The scientific novelty. Improved methods and algorithms was created for the best approximation of the surface of the Earth's lithosphere. The practical significance. Approximation algorithms of the physical surface of the Earth will be used in further research aimed at studying the characteristics of our planet planetary dynamics and their time changes. Such approaches to surface approximation are useful not only for Earth an planets Science but also in other areas where the problems arise in ellipsoidal objects modelling.
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