Gravity field of the Earth and planets - NGEO017
Title: Tíhové pole Země a planet
Form of teaching: lecture+practicals
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2025
Duration in semesters: 1
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Maximum number of enrolled students: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Repeated enrollment: 2 / 2 / 2 / 2
Guarantor: doc. RNDr. Marie Běhounková, Ph.D.
Teacher(s): doc. RNDr. Marie Běhounková, Ph.D.
Classification: Physics > Geophysics
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Annotation -
The lecture gives overview of methods describing the figure of planetary bodies. It focuses on potential theory, physical geodesy problems, description of realistic bodies, rotation and tides.
Last update: Gallovič František, prof. RNDr., Ph.D. (10.01.2019)
Aim of the course -

The lecture broadens the knowledge about the figure of the Earth and planetary bodies, including the application to planetary science.

Last update: Běhounková Marie, doc. RNDr., Ph.D. (12.05.2022)
Course completion requirements -

Course credit: Completion of the required course assignments. The submitted work may be corrected and resubmitted up to two times.

Exam: A score of at least 60% is required from the written part and the oral examination.

Last update: Běhounková Marie, doc. RNDr., Ph.D. (29.08.2026)
Literature -

M. Burša, K. Pěč: Tíhové pole a dynamika Země. Academia, Praha, 1988.

W.A. Heiskanen, F.A. Vening Meinesz: The Earth and Its Gravity Field. McGraw Hill, New York, 1958.

Kaula, W. M: Tidal dissipation by solid friction and the resulting orbital evolution. Rev. Geophys. 2.4, pp. 661–685, 1964.

P. Melchior: The Tides of the Planet Earth. Pergamon Press, Oxford, 1983.

H. Moritz: The Figure of the Earth. Theoretical Geodesy and the Earth’s Interior. Karlsruhe: Herbert Wichmann, 1990.

C.D. Murray, S.F. Dermott: Solar System Dynamics, Cambridge University Press, 1999.

O. Novotný: Motions, Gravity Field and Figure of the Earth. Lecture notes. UFBA, Salvador, Bahia, 1998.

R. Sabadini, B. Vermeersen: Application of Normal Mode Relaxation Theory to Solid-Earth Geophysics. Kluwer Academic Publisher, 2004.

G. Schubert et al. Treatise on Geophysics. Elsevier, 2007.

H. Takeuchi, and M. Saito: Seismic Surface Waves. Methods in Computational Physics: Advances in Research and Applications 11, pp. 217–295, 1972.

D.L. Turcotte, R. J. Willemann, W. F. Haxby, and J. Norberry: Role of membrane stresses in the support of planetary topography. Journal of Geophysical Research: Solid Earth 86.B5, pp. 3951–3959, 1981.

D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii. Quantum theory of angular momentum: irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols. World Scientific, Singapore, 1988.

J. Wahr: Geodesy and Gravity, 1996.

A.B. Watts. Isostasy and flexure of the lithosphere. Cambridge University Press, 2001.

Last update: Běhounková Marie, doc. RNDr., Ph.D. (12.05.2022)
Teaching methods -

Lecture + exercises

Last update: Běhounková Marie, doc. RNDr., Ph.D. (12.05.2022)
Syllabus -

1) Observational techniques. Gravity meters, absolute and relative meters, pendulums, and free-fall meters. Positioning and levelling. Space techniques.

2) Potential theory. Poisson's and Laplace's equations. The solution to Laplace's equation for planar, cylindrical, and spherical problems. Spherical harmonics, properties of spherical harmonics. Additional theorem. Gravitational potential from known structure, Helmert's condensation method, and higher-order methods.

3) Gravity field and potential of planets. External gravity field and potential for spherically/elliptically symmetric rotating bodies. Clairaut's differential equation, Darwin-Radau relation.

4) Realistic bodies. Equipotential surfaces, geoid, and spheroid. Normal gravity. Bruns's theorem, Stoke's formula. Geoid of the Earth, moons, and planets in the solar system.

5) Interpretation of observed gravity anomalies. Free-air and Bouguer reductions. Isostasy, Pratt-Hayford and Airy/Heiskanen isostasy. Vening Meinesz regional isostatic system. Isostatic reductions. Lithospheric bending, dynamic topography, long-wavelength geoid. Correlation of topography and geoid.

6) Rotation and rotational potential. Earth's rotation and its changes. Liouville's equations. Precession and nutation; dynamical flattening. Free nutation; Euler's and Chandler's periods. Changes in the length of the day.

7) Tides and tidal potential. Derivation of the tidal potential and its properties. Tidal effects on an elastic Earth; Love numbers and their importance for determining the elastic properties of the Earth.

Last update: Běhounková Marie, doc. RNDr., Ph.D. (12.05.2022)