EarthEllipsoidCoordinates 2025-12-04 06:24:06 2025-12-04 06:24:06 Topic geodetic latitude % this is the default PhysicsLibrary preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{pgfplots} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \pgfplotsset{compat=1.18} \subsection{Earth Ellipsoid Coordinates} The Earth is more accuratley modelled as an oblate ellipsoid of revolution. If the symmetry axis is taken as $OZ$ the Cartesian equation with respect to its center is \begin{equation} \frac{X^2}{a^2} + \frac{Y^2}{a^2} + \frac{Z^2}{b^2} = 1, \,\,\,\,\, a > b . \end{equation} The definition of longitude $\lambda$ is exactly the same as on the sphere. The \textbf{geodetic latitude} $\phi$, which we will siomply call latitude, is the angle at which the normal at $P$ intersects the equatorial plane $(Z = 0)$. \begin{tikzpicture} \begin{axis}[hide axis,unit vector ratio=1 1 1, width=12cm, declare function={a=2;b=1.5;c=1;}] \addplot3[surf,shader=interp,colormap/blackwhite, samples=51,samples y=51, z buffer=sort,domain=0:360,domain y=-90:90] ({a*cos(x)*cos(y)},{b*sin(x)*cos(y)},{c*sin(y)}); \end{axis} \end{tikzpicture} \begin{thebibliography}{9} [1]Osborne, Peter. The Mercator Projections. Zenodo, 2013. \PMlinkexternal{https://doi.org/10.5281/zenodo.35392}.\\ \end{thebibliography}