CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Theoretical geodesy 3

Code Completion Credits Range Language
155TGD3 Z,ZK 5 2P+2C Czech
Garant předmětu:
Jan Holešovský
Lecturer:
Jan Holešovský
Tutor:
Jan Holešovský
Supervisor:
Department of Geomatics
Synopsis:

Vector and scalar description of gravitational field of the Earth. Properties of gravitational potential and its derivatives for basic bodies. Description of gravity field of the Earth. Normal gravity field of normal bodies. Approximation of the shape of the Earth in form of geoid or level ellipsoid. Stokes´ and Molodensky´s solution of the shape of the Earth. Consequences of this procedures for geodesy (geoid, quasigeoid, heights). Construction and models of (quasi)geoid. Physical priciples of gravity surveying.

Requirements:

155TGD1

Credit - 5 exercises (1 measurement, 4 computational exercises), passing of 3 tests during the term.

Exam - written and oral part.

Syllabus of lectures:

1. Newton´s law of gravitation. Gravitational field and its vector and scalar description.

2. Properties of gravitational potential and its derivatives. Gravitational potential of basic bodies.

3. Application of gravitational potential and its derivatives - direct and inverse gravimetric problem.

4. Gravitational potential of the Earth. Spherical harmonics and surface spherical harmonics. Stokes´ coefficients of the spherical-harmonic expansion of gravitational potential of the Earth.

5. Centrifugal field of the Earth rotation. Gravity field of the Earth, equipotential surfaces. Bruns´ theorem. Geoid. Time variations of gravity field of the Earth.

6. Normal gravity field of normal bodies. Spheroids, level ellipsoid. Normal potential, normal gravity. Geodetic Reference System GRS80.

7. Anomalous gravity field. Fundamental equation of physical geodesy. Stokes´ solution of the shape of the Earth.

8. Gravity reductions and their properties.

9. Deflections of the vertical on the geoid. Formula of Vening Meinesz.

10. Molodensky´s solution of the shape of the Earth. Molodensky´s normal heights a orthometric heights. Quasigeoid. Global a local (quasi)geoid. Models of the (quasi)geoid.

11. Gravity surveying - balistic and pendulum methods.

12. Gravity surveying - relative methods (static a superconductive). Gravity systems.

Syllabus of tutorials:

1. Gravity measurement.

2. Gravitational field of the homogeneous sphere.

3. Direct and inverse gravimetric problem.

4. Surface spherical harmonics, Legendre´s associated functions.

5. Normal gravity field, equipotential surfaces.

6. Local geoid for the territory of the Czech Republic.

7. Normal heights.

Study Objective:

Student will understand the description of gravity field of the Earth, the methods of determination of the shape of the Earth (geoid, quasigeoid), physical based definitions of heights and basic principals of gravity surveying.

Study materials:

Zeman A.: Fyzikální geodézie. ČVUT 2010. ISBN 978-80-01-04599-2.

Zeman A.: Fyzikální geodézie. Teorie výšek a výškové systémy. Doplňkové skriptum. ČVUT 2008. ISBN 80-01-02733-3.

Cimbálník M., A. Zeman, J. Kostelecký: Základy vyšší a fyzikální geodézie. ČVUT 2007. ISBN 978-80-01-03605-1.

Heiskanen W. A., H. Moritz: Physical geodesy. W. H. Freeman and Company 1967. ISBN 978-0716702337.

Hofmann-Wellenhof B., H. Moritz: Physical geodesy. Springer 2006. ISBN 978-3211335444.

Note:
Further information:
https://geo.fsv.cvut.cz/gwiki/155TGD3_Teoretická_geodézie_3
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet5635506.html