11 G G Stokes 1819 1903 \u00f2 Coordinate system local 14 LEESSE 1012 Lecture 25

G. G. Stokes (1819 - 1903)

òCoordinate system: local 14 LE/ESSE 1012–Lecture 25 ©MJadidi Dr Spiros Pagiatakis, 2017 UP EAST NORTH (Z) (X) (Y) UP UP UP GEOCENTRE LOCAL COORDINATE SYSTEM

òCOORDINATE SYSTEM: GEOCENTRIC 15 LE/ESSE 1012–Lecture 25 ©MJadidi Dr Spiros Pagiatakis, 2017

X (Greenwich) Y zpxp ypλφZ (Spin axis) Geocentric Coordinate Systems

Geodetic Latitude & Longitude, height òGeodetic Longitude λòthe Angle between the prime meridian and the meridian passing through the point. òGeodetic Latitude ϕòthe angle between the equator plane and the normal to the ellipsoid passing through p. òEllipsoid height (geodetic) hòthe distance along the normal between the point pand the ellipsoid. 17

Great Circle Distance AD 18 ΔφReReR R A C ΔλD Length on a Meridian: same for all latitudes AC(m)=Δm = Re(m)Δφ(rad)Length on a Parallel: varies with latitude CD(m)=Δp= R Δλ=RecosφΔλAD=AC2+CD2Pay attention to unit

Spatial Referencing Process 19 Earth Earth Geoid Ellipsoid Datum Projection Coordinate System

Ellipsoid òA mathematical approximation to the shape of the Earth, defined by two parameters of a, b, (and f, and e). 20 a b 22()flattening: , first eccentricity squared: 2abfeffa−==a b Equator

Geoid and Ellipsoid òThe Geoid is an equipotential surface of the Earth gravity field that most closely approximates the mean sea level.