FUNDAMENTALS OF GEODESY
Objectives:
To impart knowledge on fundamentals of Geodesy and develop skills in computer programming.

  1. Introduction (3 hours)

  2. The System of Natural Coordinates (6 hours)
    1. Newtonian Gravitational Attraction
    2. The Gravity Potential
    3. Level Surfaces and Plumb Line
    4. Natural Coordinates

  3. Approximation the Natural System of Coordinates (6 hours)
    1. The Concept of a Best Fitting Ellipsoid
    2. Basic Ellipsoidal Geometry
    3. Coordinate Systems on the Ellipsoid
    4. Transformation between Cartesian and Curvilinear Geodetic Coordinates
    5. Curvature and the Intrinsic Geometry of Surfaces
    6. A first Look at Curves on the Ellipsoid-Meridian and Parallel Arcs
    7. General Curves on the Ellipsoid-the Concept of Geodesy

  4. Coordinate Transformations (6 hours)
    1. Rotation and Reflection Matrices
    2. Transformation between Systems with Different Origins and Orientations
    3. Transformation between Local and Global Systems
    4. Differential Formulas for Transformation between Systems
    5. Summary of Coordinates Systems and Transformations between Them

  5. Celestial Systems (6 hours)
    1. The celestial Sphere
    2. The Horizon System
    3. The right Ascension System
    4. The Hour Angle System
    5. The Ecliptic System
    6. Transformations Between Celestial Systems

  6. Approximating an Inertial Frame of Reference (9 hours)
    1. Newton’s First Law and the Concept of an Inertial Frame
    2. The Rotation of the Earth
    3. Torques on the earth-Precession and Forced Nutation
    4. Free Nutation-Polar Motion
    5. Defining an Inertial Frame of Reference
    6. Proper Motion of Stars
    7. Effects of Linear Motion-Aberration and Parallax
    8. Fixing the Inertial Reference by Observations

  7. Time Systems (9 hours)
    1. Time and Motion
    2. Sidereal Time
    3. Universal (Solar) Time
    4. Conversion of Time
    5. Dynamic Coordinate Systems
    6. Newton and the Motion of an Earth
    7. The First Approximation
    8. The Second Approximation
    9. Computation of the Satellite Position in the CT-Systems
    10. Review of Coordinate Systems

Appendix:

  1. Basic Differential Geometry
    1. Representation of Surfaces
    2. The first Fundamental Form
    3. Geodesics
  2. Closed Formula for the Transformation of the Cartesian Coordinates x, y, z into Geodetic Co-ordinates N, 8, h
  3. Coefficient Matrices for Differential Transformation Formulae
  4. Transformation of a Star Position from Epoch ≅ to Epoch T

Lab:
Computer programming in ‘C or C++’ in five lab exercises.

  1. Celestial sphere; Astronomical triangle, computations
  2. Computer programs for calculation of elements of spherical triangles
  3. Derivation of the formulae of the ellipse, review of different ellipsoids, concept of WGS-84
  4. Transformation of Cartesian (X, Y, Z) to curvilinear geodetic coordinates (∅, λ, ђ) (computer programming)
  5. Introduction to transformation matrices
  6. Concept of WGS-84 and local ellipsoid
  7. Coordinate systems transformation between them (computer programming)
  8. Celestial system-The celestial sphere and different celestial systems (H-system, R A system, H A system, Ecliptic system)
  9. Transformation matrices from one celestial system to another (computer programming)
  10. Conversion between Sidereal time and universal (solar) time (computer programming)

Reference:

  1. P. Swartz, Class note on Fundamental of Geodesy, University of Calgary
  2. Gilbert Strang-Linear Algebra, Geodesy and GPS 199
  3. Hofmann-Wellenhof and H. Moritz, Physical Geodesy, Springer-Verlag Wein, 2005
  4. A lecture note: Coordinate system in geodesy by E.J Krakiwsky and D.E Wells, UoC December 1999.
  5. GPS-Theory and Practice by Bhofman-weldenhof, Lichenegger and Collins, Springer wein ISBN 3211828397

Assessment: Averaging of three

Evaluation Scheme:
The questions will cover all the chapters in the syllabus. The evaluation scheme will be as indicated in the table below:

S.N.

Chapter

Hours

Marks allocation*

1

1,2

9

16

2

3,4.1-4.3

9

16

3

4.4, 4.5,5

9

16

4

6

9

16

5

7

9

16

Total

45

80

*Note: There may be minor deviation in marks distribution

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