@ARTICLE{Kovalchuk_Vasyl_Comparison_2023,
 author={Kovalchuk, Vasyl and Mladenov, Ivaïlo M.},
 volume={71},
 number={5},
 journal={Bulletin of the Polish Academy of Sciences Technical Sciences},
 pages={e147058},
 howpublished={online},
 year={2023},
 abstract={In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).},
 type={Article},
 title={Comparison of main geometric characteristics of deformed sphere and standard spheroid},
 URL={http://www.czasopisma.pan.pl/Content/128622/PDF/BPASTS-03652-EA.pdf},
 doi={10.24425/bpasts.2023.147058},
 keywords={deformed sphere, standard spheroid, sphericity index, tipping (bifurcation) point for geodesics, elliptic integrals and functions},
}