Gravity field of the Earth and planet

Notes, literature, files

MS teams link

Lecture and practicals

Wednesdays from 10.40, Department of geophysics lecture room, Troja (floor 11).

Lectures

1. Introduction. Historical review. Reference systems. Preliminaries and revision, coordinates systems. Euler’s equations.
2. Potential theory. Gravitational potential. Poisson’s and Laplace’s equations.
3. Legendre’s polynomials and spherical harmonics. Applications, gravitational potential for known density, gravitational potential of elliptic homogeneous body.
4. Interpretation of gravity anomalies on degrees 0, 1, 2. Elliptically symmetric rotating bodies. Clairaut’s differential equation.
5. Clairaut’s, Radau’s and Darwin-Radau’s equations.

Syllabus

1. Observational techniques. Gravity meters, absolute and relative meters, pendulums and free fall meters. Positioning and leveling. Space techniques.
2. Potential theory. Poisson’s and Laplace’s equations. Solution to Laplace’s equation for planar, cylindrical and spherical problems. Spherical harmonics, properties of spherical harmonics. Additional theorem, Helmert’s condensation method.
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. Vennig Meinesz regional isostatic system. Isostatic reductions. Lithospheric bending, dynamic topography, long-wavelength geoid. Correlation of topography and geoid.
6. Revolution of the Earth and planetary bodies. 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 day.
7. Tides and tidal potential. Derivation of the tidal potential, its properties. Tidal effects on an elastic Earth; Love numbers and their importance for determining the elastic properties of the Earth.

Practicals

Literature

• 13. 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.
• 16. Melchior: The Tides of the Planet Earth. Pergamon Press, Oxford 1983.
• C.D. Murray, S.F. Dermott: Solar System Dynamics, Cambridge University Press, 1999.
• 15. Novotný: Motions, Gravity Field and Figure of the Earth. Lecture notes. UFBA, Salvador, Bahia 1998.
• 13. Pick, J. Pícha, V. Vyskočil: Úvod ke studiu tíhového pole Země. Academia, Praha 1973.
• 18. Sabadini, B. Vermeersen: Application of normal Mode Relaxation Theory to Solid-Earth Geophysics. Kluwer Academic Publisher, 2004.
• 10. Wahr: Geodesy and Gravity, 1996.
• Treatise on Geophysics. Editor-in-Chief G. Schubert. Elsevier 2007, ISBN 978-0-444-52748-6