basic geodesy.pdf
- 1. Geodesy, GE 202 Kutubuddin ANSARI kutubuddin.ansari@ikc.edu.tr Lecture 1, Sep 27, 2016 Basic of Geodesy
- 2. Geodesy :- Geo - Earth desy - The study of “The study of the Earth” Geodesy is the science of the measurement and mapping of the earth’s surface
- 3. Merriam-Webster:a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field.
- 4. • Geometrical geodesy is concerned with describing locations in terms of geometry. Consequently, coordinate systems are one of the primary products of geometrical geodesy. •Physical geodesy is concerned with determining the Earth’s gravity field, which is necessary for establishing heights. •Satellite geodesy is concerned with using orbiting satellites to obtain data for geodetic purposes. Types of Geodesy
- 5. R ψ ΔG R = ΔG /Ψ Spherical Model of the Earth
- 6. Eratosthenes had observed that on the day of the summer solstice (20-22 June), the midday sun shone to the bottom of a well in the Ancient Egyptian city of Swenet (known in Greek as Syene). Eratosthenes Egypt about 240 BC Spherical Model of the Earth
- 8. •He knew that at the same time, the sun was not directly overhead at Alexandria; instead, it cast a shadow with the vertical equal to 1/50th of a circle (7° 12'). •He also knew that Alexandria and Syene were 500 miles apart •To these observations, Eratosthenes concluded that the circumference of the earth was 50 x 500 miles, or 25000 miles. Spherical Model of the Earth
- 9. •The accepted value along the equator is 24,902 miles, but, if you measure the earth through the poles the value is 24,860 miles •He was within 1% of today’s accepted value •Eratosthenes' conclusions were highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of years afterwards. Spherical Model of the Earth
- 10. How Do We Define the Shape of the Earth? We think of the earth as a sphere It is actually a spheroid, slightly larger in radius at the equator than at the poles
- 11. The Ellipsoid An ellipse is a mathematical figure which is defined by Semi-Major Axis (a) and Semi-Minor Axis (b) or Flattening (f) = (a - b)/a It is a simple geometrical surface Cannot be sensed by instruments b a
- 12. Ellipsoid or Spheroid O X Z Y a a b Rotational axis Rotate an ellipse around an axis
- 13. Selection of the Spheroid is what determines the size of the Earth
- 14. The Real Earth (The Geoid)
- 15. Europe N. America S. America Africa Topography An ellipsoidal-earth model is no longer tenable at a high level of accuracy. The deviation of the physical measurements refer from the ellipsoidal model can no longer be ignored. The geoid anomaly is the difference between the geoid surface and a reference ellipsoid The Real Earth (Geoid)
- 16. What is the Geoid? • “The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, global mean sea level.” • Can’t see the surface or measure it directly. • Modeled from gravity data.
- 17. Ellipsoid and Geoid Ellipsoid • Simple Mathematical Definition • Described by Two Parameters • Cannot be 'Sensed' by Instruments Geoid • Complicated Physical Definition • Described by Infinite Number of Parameters • Can be 'Sensed' by Instruments
- 18. Earth surface Ellipsoid Sea surface Geoid Since the Geoid varies due to local anomalies, we must approximate it with a ellipsoid Ellipsoid and Geoid
- 19. O1 Europe N. America S. America Africa Topography N Ellipsoid and Geoid
- 20. Which ellipsoid to choose ? O2 O1 Europe N. America S. America Africa N Topography N Ellipsoid and Geoid
- 21. Common Ellipsoid The best mean fit to the Earth Europe N. America S. America Africa N Topography A = 6,378,137.000 m 1/f = 298.2572236
- 22. Unfortunately, the density of the earth’s crust is not uniformly the same. Heavy rock, such as an iron ore deposit, will have a stronger attraction than lighter materials. Therefore, the geoid (or any equipotential surface) will not be a simple mathematical surface. Ellipsoid and Geoid Heights
- 23. Heighting •The equipotential surface is forced to deform upward while remaining normal to gravity. This gives a positive geoid undulation. •Conversely, a mass shortage beneath the ellipsoid will deflect the geoid below the ellipsoid, causing a negative geoid undulation. Ellipsoid Ellipsoid P P H H Geoid Geoid h h Topography Topography
- 24. h = H + N h = H + N h = H + N h = H + N Ellipsoid Ellipsoid h h P P Topography Topography H H Geoid Geoid N N N = Geoidal Separation H = Height above Geoid (~Orthometric Height) h = Ellipsoidal height Heighting Orthometric Height (h) “ perpendicular vertical distance between the geoid and land surface”
- 25. Heighting The height difference between ellipsoid and geoid is called the geoidal undulation To obtain orthometric heights, the geoidal undulation must be accounted for Ellipsoid Ellipsoid P P H H Geoid Geoid N N N = Geoidal Separation h h Topography Topography
- 26. Latitude and Longitude Lines of latitude are called “parallels” Lines of longitude are called “meridians” The Prime Meridian passes through Greenwich, England
- 27. Latitude and Longitude in N. America 90 W 120 W 60 W 30 N 0 N 60 N
- 28. Length on Meridians and Parallels 0 N 30 N ∆φ Re Re R R A B C ∆λ (Lat, Long) = (φ, λ) Length on a Meridian: AB = Re ∆φ (same for all latitudes) Length on a Parallel: CD = R ∆λ = Re ∆λ Cos φ (varies with latitude) D
- 29. Any set of numbers, usually in sets of two or three, used to determine location relative to other locations in two or three dimensions Coordinate systems
- 30. Global Cartesian Coordinates (x,y,z) O X Z Y Greenwich Meridian Equator • •A system for the whole earth •Non manageable and difficult to relate to other locations when translated to two dimensions •The z-coordinate is defined as geometrically
- 31. Geographic Coordinates (φ, λ, z) • Latitude (φ) and Longitude (λ) defined using an ellipsoid, an ellipse rotated about an axis • Elevation (z) defined using geoid, a surface of constant gravitational potential
- 32. Origin of Geographic Coordinates (0,0) Equator Prime Meridian
- 33. Coordinate System (φo,λo) (xo,yo) X Y Origin A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin
- 34. (φ, λ) (x, y) Map Projection Coordinate System