Semester: 6 / Spring
Lectures/Classes: 30 / 30 hours
Field of study: Geodesy and Cartography
Study cycle: 1st cycle
Type of course: compulsory
Prerequisites: Math Analysis, Physics, Geodetic Reference Frames
Contact person: mgr inż. Mateusz Drożdżewski; e-mail:
Short description: The gravitational field of the Earth, geoid, quasigeoid and methods of their determination. Height systems, precise leveling and geodetic vertical networks. Gravimetric measurements and gravimetric networks. The integration of ground-based measurement methods in the gravitational field of the Earth.
Full description: 1. Gravity field of the Earth: gravity vector, potential and acceleration of gravity, equipotential surfaces, geoid, vertical deflection, curvatures of the equipotential surfaces and lines of gravity forces, Laplace and Poisson equations, vertical gradient of the gravity, Eötvös tensor, potential in the form of a series of spherical functions, temporal variations of the gravity field. 2. Gravitational normal field: geodetic reference system GRS80, world geodetic system WGS84, normal potential, normal gravity vector, normal geodetic latitude, gravity on the ellipsoid, transfer of gravity from ellipsoid to earth surface, physical determination of ellipsoidal height. 3. Gravitational Earth’s model EGM: EGM96 and EGM2008 models, potential, gravity vector, astronomic latitude and longitude, orthometric height, geoid height, height anomaly, normal height, vertical deflection. 4. Height systems: orthometric height - Helmert and Poincare-Prey, normal height - telluroid, quasigeoid and height anomaly, quasigeoid height and vertical deflection components interpolation in the PL-geoid-2011 model, dynamical height, precise leveling corrections, national spatial reference system, vertical networks. 5. Residual gravitational field of the Earth: disturbing potential and gravity, gravity anomaly, height anomaly, geoid height and vertical deflection. 6. Quasigeoid modeling: Molodensky’s boundary value problem of physical geodesy, the concept of height quasigeoid modeling based on Brovar’s series: global, gravimetric and terrain componets plus polynomial trend and random rest, the GGI method, precise 5 mm quasigeoid modeling on the LGOM area, precise 5 mm astronomical-grawimetric levelling on the LGOM area. 7. Integration of geodetic terrestrial measurement techniques in gravitational field: Totalstation/GNSS/EGM, Laserscanner/GNSS /EGM, UAV/Totalstation/GNSS/ EGM, applications in precision geometry measurement of 3D objects with direct geocentric georeferencing. 8. Gravimetry and gravimetric networks: ground gravimetry - absolute and relative measurements, gravimetric networks, inertial ground and air gravimetry, satellite gravimetry – SST method, CHAMP and GRACE satellites, surface, air and satellite gradiometry, GOCE satellite. 9. Basics of modeling of the gravity field and geoid: boundary value problems of physical geodesy, gravimetric and GNSS-leveling geoids and their fitting methods, spectral combination, collocation and remove-compute-restore techniques, global modeling of the gravity field and geoid, EGM2008, GOCE and other models.
Bibliography: Barlik M., Pachuta A. Geodezja fizyczna i grawimetria geodezyjna. Wyd. PW 2007. Czarnecki K. Geodezja współczesna. PWN, Warszawa 2014. Hofmann-Wellenhof B. Moritz H. Physical Geodesy. Springer 2005. Łyszkowicz A. Geodezja fizyczna. Wyd. UWM, Olsztyn 2012. Osada E. Geodezyjne układy odniesienia. UxLan, Wrocław 2016. Osada E. Geodezyjne pomiary szczegółowe. UxLan, Wrocław 2014. Torge W., Muller J. Geodesy. DE GRUYTER 2012. Torge W. Gravimetry. DE GRUYTER 1989.
Learning outcomes: Knowledge The student has knowledge of the: • gravity field of the Earth, geoid, quasigeoid and methods of their determination, • height systems, precise leveling and geodetic vertical networks, • gravimetric measurements and gravimetric networks, • integration of ground-based measurement methods in the gravitational field of the Earth. Skills Student is able to: • determine of the geoid/quasigeoid height and vertical deflection components in the geoid/quasigeoid grid models and Earth’s gravity models, • determine of the systematic corrections in precise levelling and gravimetric networks, • perform integrated in the gravitational field measurements of geometry and geocentric georeference of terrestrial three-dimensional objects. Social competences Student demonstrates understanding of the impact and the importance of continuous training and improving professional competence and is aware of and understands the validity of the non-technical aspects of the surveyor.
Assessment methods and assessment criteria: Exercise 50%, Lecture 50 %

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