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 EllipsoidMeridian and Parallel Arcs
 General Curves on the Ellipsoidthe 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 earthPrecession and Forced Nutation
 Free NutationPolar Motion
 Defining an Inertial Frame of Reference
 Proper Motion of Stars
 Effects of Linear MotionAberration 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 CTSystems
 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 Coordinates 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 WGS84
 Transformation of Cartesian (X, Y, Z) to curvilinear geodetic coordinates (∅, λ, ђ) (computer programming)
 Introduction to transformation matrices
 Concept of WGS84 and local ellipsoid
 Coordinate systems transformation between them (computer programming)
 Celestial systemThe celestial sphere and different celestial systems (Hsystem, 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 StrangLinear Algebra, Geodesy and GPS 199
 HofmannWellenhof and H. Moritz, Physical Geodesy, SpringerVerlag Wein, 2005
 A lecture note: Coordinate system in geodesy by E.J Krakiwsky and D.E Wells, UoC December 1999.
 GPSTheory and Practice by Bhofmanweldenhof, 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 
3,4.14.3 
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
