The Conformal Mapping between the Globally as well as Locally of the Earth (Ellipsoid) and the Cartesian Coordinates

Abstract

We investigate the geometrical properties of the ellipsoid ( by ellipsoid we mean an ellipsoid of revolution) globally as well as locally. on this curved surface we study the basic   transformation between   polar and curvilinear coordinates . the series expansion contain a sufficient number of terms to guarantee computational accuracies at maximum level .we start by deriving the length of the meridian arc form equator to a point with arbitrary latitude. The computation as fundamental to all conformal mapping. we will derive   the   explicit formulas for   the   transformation: (latitude   ,longitude)   = (f,l) ® (x, y) and (x, y) ® (f, l) .These formulas are adopted for the Universal Transverse Mercator Mapping (UTM) . As an application of this research work we give examples for each case of work , and we take three locations in the Misurata City which are the Misurata University , the Faculty of Science , and the Stadium in Misurata City.