EarthEllipsoidCoordinates 2025-12-04 06:24:06 2026-09-07 15:40:20 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} % 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 \subsection{Earth Ellipsoid Coordinates} The Earth is more accurately modeled as an oblate ellipsoid of revolution. If the symmetry axis is taken as $OZ$, then 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, \qquad a>b. \end{equation} The definition of longitude $\lambda$ is exactly the same as on the sphere. The geodetic latitude $\phi$, which we will simply call latitude, is the angle at which the normal at $P$ intersects the equatorial plane $(Z=0)$. \centering \includegraphics[width=0.85\textwidth,keepaspectratio]{EarthEllipsoidCoordinates.png} {\small Figure 1. Cross-section of an oblate Earth ellipsoid showing the geodetic latitude $\phi$.} \begin{thebibliography}{9} \bibitem{Osborne2013} This article is a derivative work of material in: P. Osborne, \emph{The Mercator Projections}. Zenodo, 2013. \PMlinkexternal{DOI: 10.5281/zenodo.35392}{https://doi.org/10.5281/zenodo.35392} \end{thebibliography}