Introduction to Geodesy-Types, Shape of earth
- 1. Introduction to Geodesy Diploma in Surveying , Year I Semester II Geodesy GDS102 Tutor: Mim Prasad Phuyel Asst. Lecturer at Department of Civil Engineering and Surveying Jigme Namgyel Engineering College Royal University of Bhutan UNIT I
- 2. Prepared by Mim Definition of Geodesy •Geo- Earth •desy- Study •“The Science concerned with determining size and shape of the earth”. mimphuyel.jnec@rub.edu.bt
- 3. Prepared by Mim Definition of Geodesy •Geodesy is the science which deals with the methods of precise measurements of elements of the surface of the earth and their treatment for the determination of geographic positions on the surface of the earth. It also deals with the theory of size and shape of the earth. •“It is the science of the measurement and mapping of the earth’s surface” (F.R Helmert, 1880) •It also includes the determination of earth’s external gravity field, as well as the surface of the ocean floor.
- 4. Prepared by Mim Definition of Geodesy •Physical Geodesy : Detailing the Earth’s gravity field •Geometric Geodesy: Concerned with determining positional relationship •Satellite Geodesy: The observations and computation techniques by the use of precise measurements to, from, or between artificial satellites to solve geodetic problems. • Satellite geodesy is concerned with using orbiting satellites to obtain data for geodetic purposes.
- 5. Prepared by Mim The Shape of Earth This is HOW Earth looks Like…. ….But is Really ….THIS
- 6. Prepared by Mim Problems of Geodesy • To determine the figure (geometry) and external gravity field of the earth and of the other celestial bodies as a function of time. • To determine the mean earth ellipsoid from parameters observed on and exterior to the earth’s surface • The irregular surface of the solid earth (continents and ocean floor) is incapable of being represented by a simple mathematical relation • It is therefore described point wise by the use of coordinates of the control points. • On the other hand Ocean surface follow simpler principle as they form a part of a level (equipotential) surface (surface of constant gravity potential) of the earth’s gravity field. This surface may be extended under the continents and then identify it as a mathematical figure of the earth designating the level surface known as Geoid.
- 7. Prepared by Mim The figure of the Earth, early conceptions • In early days, the most common conception of the figure of the Earth was that the Earth is a flat disc. • Later, people had observed how, during a lunar eclipse, the Earth cast her shadow on the surface of the Moon. • They also observed that a lunar eclipse that was high in the sky at one end of the Mediterranean happened near the horizon at the other end. • Assuming that this was one and the same event, this could only mean that the Earth’s surface must be curved at least in the east-west direction.
- 8. Prepared by Mim Historical Development of Geodesy How did the concept of Geodesy started? What is the actual shape of earth ? Who thought about the shape of earth?
- 9. Prepared by Mim Spherical Model of Earth •Eratosthenes had observed that on the day of summer solstices (20-22 June), the mid-day sun shone to the bottom of well in the ancient Egyptian city of Syene.
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- 11. Prepared by Mim • He Knew that at the same time, the sun was not directly overhead at Alexandria, instead it cast a shadow with vertical equal to 1/50th of circle (7 degree 12 minutes) • 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 • The accepted value along the equator is 24,902 miles but if you measure the earth through poles the value is 24,860 miles • He was within 1% of today’s accepted value
- 12. Prepared by Mim Ellipsoidal Earth model • N. Copernicus (1473-1543) • J. Kepler(1571-1630): Discovered laws of planetary motion • Galileo Galilei (1564-1642) : Modern mechanics (law of falling bodies, law of pendulum motion) • 1n 1666, astronomer J.D Cassini observed the flattening of the poles of Jupiter. • Isaac Newton (1643-1727) and Christian Huygens (1629-1695) developed earth models flattened at the poles and founded on the principles of physics
- 13. Prepared by Mim Newton’s Model • Newton obtained a rotational ellipsoid as an equilibrium figure for a homogenous fluid, rotating earth based on the validity of the law of universal gravitation. • The flattening f: f=(a-b)/a a=semi-major axis, b=semi-minor axis As per Newton f=1/230 He also postulated that gravity acceleration increases from the equator to the poles and is proportional to 𝑠𝑖𝑛2∅, 𝑤ℎ𝑒𝑟𝑒 ∅ = 𝑔𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒𝑠
- 14. Prepared by Mim Huygen’s Model • As per Huygen, he shifts the source of earths attractive forces to the centre of the earth and develops a rotationally symmetric equilibrium surface which possesses a meridian curve of fourth order with f=1/576
- 15. Prepared by Mim Current Understanding
- 16. Prepared by Mim The Geoid and Ellipsoid
- 17. Prepared by Mim 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
- 18. Prepared by Mim The Ellipsoid The ellipsoid is a smooth, symmetric surface that approximates the shape of the Earth and is used as a reference surface for mapping and surveying.
- 19. 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)
- 20. Prepared by Mim The Geoid •Geoid- The equipotential surface that mostly corresponds the mean sea level (MSL). •The geoid takes into account the Earth's irregularities and is used as a reference surface for measuring elevations and for determining the Earth's gravity field.
- 21. 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
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- 23. Prepared by Mim Since the Geoid varies due to local anomalies, we must approximate it with a ellipsoid
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- 25. Prepared by Mim Reference Ellipsoid •Reference ellipsoids are primarily used as a surface to specify point coordinates such as latitudes (north/south), longitudes (east/west) and elevations (height). •The most common reference ellipsoid in cartography and surveying is the World Geodetic System (WGS84). •Study the characteristics of WGS84 (Coursework)
- 26. Prepared by Mim Ellipsoid and Geoid Heights •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. 𝐹 = 𝐺 𝑀𝑎𝑀𝑏 𝑟2
- 27. 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 P H Geoid h Topography
- 28. Heighting
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- 30. Prepared by Mim Datum •Datum in surveying is a reference point or surface that is used to define the location of points on the Earth's surface. •Geoids, ellipsoids, and local datums are all different types of datums that are used in surveying. •Horizontal and vertical datums are also used to define positions and heights, respectively.
- 31. Prepared by Mim Datum • Horizontal datums give us the capability to measure distances and directions across the surface of the earth. Most horizontal datums define a zero line at the equator from which we measure north and south (latitudes) • There is also a zero line at the Greenwich Meridian from which we measure east and west (longitudes). • Together these lines provide a reference for latitude and longitude expressed in decimal degrees. These latitudes and longitude positions (Geographic Coordinate Systems) are based on a spheroid or ellipsoid surfaces that approximate the surface of the earth – a datum.
- 32. Prepared by Mim Bhutan National Geodetic datum Attributes : • Ellipsoid: GRS 1980 • Prime meridian: Greenwich • Data source: EPSG
- 33. Prepared by Mim Arc Measurement The measure of an arc can be found by dividing that arc's length (l) by the circle's radius (r). Arc length (l) the distance along the part of the circumference of any circle or any curve (arc) Circumference C=2πr
- 34. Prepared by Mim End of Unit I