FUNDAMENTALS OF GEODESY
Objectives:
To impart knowledge on fundamentals of Geodesy and develop skills in computer programming.
- Introduction (3 hours)
- The System of Natural Coordinates
(6 hours)
- Newtonian Gravitational Attraction
- The Gravity Potential
- Level Surfaces and Plumb Line
- Natural Coordinates
- Approximation the Natural System of Coordinates
(6 hours)
- The Concept of a Best Fitting Ellipsoid
- Basic Ellipsoidal Geometry
- Coordinate Systems on the Ellipsoid
- Transformation between Cartesian and Curvilinear Geodetic Coordinates
- Curvature and the Intrinsic Geometry of Surfaces
- A first Look at Curves on the Ellipsoid-Meridian and Parallel Arcs
- General Curves on the Ellipsoid-the Concept of Geodesy
- Coordinate Transformations
(6 hours)
- Rotation and Reflection Matrices
- Transformation between Systems with Different Origins and Orientations
- Transformation between Local and Global Systems
- Differential Formulas for Transformation between Systems
- Summary of Coordinates Systems and Transformations between Them
- Celestial Systems
(6 hours)
- The celestial Sphere
- The Horizon System
- The right Ascension System
- The Hour Angle System
- The Ecliptic System
- Transformations Between Celestial Systems
- Approximating an Inertial Frame of Reference
(9 hours)
- Newton’s First Law and the Concept of an Inertial Frame
- The Rotation of the Earth
- Torques on the earth-Precession and Forced Nutation
- Free Nutation-Polar Motion
- Defining an Inertial Frame of Reference
- Proper Motion of Stars
- Effects of Linear Motion-Aberration and Parallax
- Fixing the Inertial Reference by Observations
- Time Systems (9 hours)
- Time and Motion
- Sidereal Time
- Universal (Solar) Time
- Conversion of Time
- Dynamic Coordinate Systems
- Newton and the Motion of an Earth
- The First Approximation
- The Second Approximation
- Computation of the Satellite Position in the CT-Systems
- Review of Coordinate Systems
Appendix:
- Basic Differential Geometry
- Representation of Surfaces
- The first Fundamental Form
- Geodesics
- Closed Formula for the Transformation of the Cartesian Coordinates x, y, z into Geodetic Co-ordinates N, 8, h
- Coefficient Matrices for Differential Transformation Formulae
- Transformation of a Star Position from Epoch ≅ to Epoch T
Lab:
Computer programming in ‘C or C++’ in five lab exercises.
- Celestial sphere; Astronomical triangle, computations
- Computer programs for calculation of elements of spherical triangles
- Derivation of the formulae of the ellipse, review of different ellipsoids, concept of WGS-84
- Transformation of Cartesian (X, Y, Z) to curvilinear geodetic coordinates (∅, λ, ђ) (computer programming)
- Introduction to transformation matrices
- Concept of WGS-84 and local ellipsoid
- Coordinate systems transformation between them (computer programming)
- Celestial system-The celestial sphere and different celestial systems (H-system, R A system, H A system, Ecliptic system)
- Transformation matrices from one celestial system to another (computer programming)
- Conversion between Sidereal time and universal (solar) time (computer programming)
Reference:
- P. Swartz, Class note on Fundamental of Geodesy, University of Calgary
- Gilbert Strang-Linear Algebra, Geodesy and GPS 199
- Hofmann-Wellenhof and H. Moritz, Physical Geodesy, Springer-Verlag Wein, 2005
- A lecture note: Coordinate system in geodesy by E.J Krakiwsky and D.E Wells, UoC December 1999.
- 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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