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.
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.