Exact and heuristic formulae to compute the geodetic height from the ellipse equation  

作　　者：Mohamed Eleiche Ahmed Hamdi Mansi 

机构地区：[1]Construction Department,Faculty of Engineering,Egyptian Russian University,Cairo,Egypt [2]Istituto Nazionale di Geofisica e Vulcanologia,Sezione di Pisa,Pisa,Pl,Italy

出　　处：《Geodesy and Geodynamics》2024年第2期150-155,共6页大地测量与地球动力学（英文版）

摘　　要：The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy.The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates.This research analyzes this influence and how it can contribute to their solutions.The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation.In addition,a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed,which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %.The calculation is stable,and the cost is low.

关 键 词：Ellipse equation Geodetic height Heuristic geodetic height 

分 类 号：P226[天文地球—大地测量学与测量工程]