1. Lecture 11: Geometry of the Ellipse 25 February 2008 GISC-3325

2. Class Update Next exam 12 March 2008 Labs 1-4 due today! Homework 2 due 3 March 2008 Will have exams graded by next Monday –Will post solutions to class web page

3. Note on orthometric heights Orthometric height differences are provided by leveling ONLY when there is parallelism between equipotential surfaces. –Over short distances this may be the case. To account for non-parallelism we use geopotential numbers in computations. In general, geopotential surfaces are NOT parallel in a N-S direction but are E-W

4. Level Project

5. Gravity values for points

6. Helmert Orthometric Heights

9. Geometry of the Ellipsoid Ellipsoid of revolution is formed by rotating a meridian ellipse about its minor axis thereby forming a 3-D solid, the ellipsoid. Modern models are chosen on the basis of their fit to the geoid. –Not always the case!

10. Parameters a = semi-major axis length b = semi-minor axis length f = flattening = (a-b)/a e = first eccentricity = √((a 2 -b 2 )/a 2 ) e’ = second eccentricity = √((a 2 -b 2 )/b 2 )

11. THE ELLIPSOID MATHEMATICAL MODEL OF THE EARTH b a a = Semi major axis b = Semi minor axis f = a-b = Flattening a N S

12. THE GEOID AND TWO ELLIPSOIDS GRS80-WGS84 CLARKE 1866 GEOID Earth Mass Center Approximately 236 meters

13. NAD 83 and ITRF / WGS 84 ITRF / WGS 84 NAD 83 Earth Mass Center 2.2 m (3-D) dX,dY,dZ GEOID

18. Geodetic latitude Geocentric latitude Parametric latitude Unlike the sphere, the ellipsoid does not possess a constant radius of curvature.

23. Radius of Curvature of the Prime Vertical