TY - JOUR
N2 - 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).
L1 - http://sd.czasopisma.pan.pl/Content/128622/PDF/BPASTS-03652-EA.pdf
L2 - http://sd.czasopisma.pan.pl/Content/128622
PY - 2023
IS - 5
EP - e147058
DO - 10.24425/bpasts.2023.147058
KW - deformed sphere
KW - standard spheroid
KW - sphericity index
KW - tipping (bifurcation) point for geodesics
KW - elliptic integrals and functions
A1 - Kovalchuk, Vasyl
A1 - Mladenov, Ivaïlo M.
VL - 71
DA - 21.09.2023
T1 - Comparison of main geometric characteristics of deformed sphere and standard spheroid
SP - e147058
UR - http://sd.czasopisma.pan.pl/dlibra/publication/edition/128622
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -