A fundamentally new era began in the study of the figure and the gravitational field of the Earth with the study of the flight of the first satellite and determining the orbits of subsequent ones. Methods for solving geodetic problems on observations of satellite can be divided into geometric and dynamic. Geometrical methods of space geodesy were the first to apply for the solution of geodetic tasks. In these methods, satellites are considered only as a high sighting target. The solution of geodetic problems by geometric methods of space geodesy was carried out on the basis of synchronous observations of the satellite from several points. Observations of satellites were carried out using photographic, radio, or laser measurement systems.

       One of the first objects of observation by geometric methods of space geodesy were satellites-cylinders Echo-1, Echo-2, PAGEOS, as well as geodetic satellites of the GEOS series. They had flash lamps placed onboard for the synchronicity of photo observations. Those methods were used in the practical implementation of the first geodetic programs of the satellite (space) triangulation. That allowed determining of the geocentric coordinates of tracking stations with high accuracy. The rapid progress in the satellite motion theory, design of special geodetic satellites, and the development of new tools for their observations (Doppler receivers, laser rangefinders, radio-dimensional systems) have provided the increasingly wide application of dynamic methods of space geodesy for the geodetic solutions. These methods are based on the calculation of the exact orbits of satellites obtained from trajectory measurements, taking into account all the forces affecting them. In this case, the parameters determined were the coordinates of the points, the parameters of the Earth’s gravitational field, the parameters of the satellite motion model, as well as some geodynamic parameters (for example, the parameters of the Earth’s rotation). Moreover, unlike the geometric methods of satellite geodesy, dynamic methods do not need simultaneous observations of the satellite and allow the determination of the position of points in the coordinate system connected with the center of mass of the Earth.

        A significant contribution to the solution of geodesic and geodynamic problems was made by the use of observations of spacecraft of global navigation satellite systems. The solution of geodynamic problems is associated with the study of dynamic processes occurring in the Earth system and the force fields causing these processes. The results of many geodynamic solutions and satellite gravity missions show that methods of space geodesy can be successfully used to determine various parameters that reflect the dynamic processes in the bowels of the Earth. At the same time, often the same satellites can be used to solve both geodetic tasks and problems of other Earth sciences. The article reflects the main stages in the progress of space geodesy methods in determining the shape and gravitational field of the Earth, as well as the use of these methods for solving problems of geophysics, geodynamics, oceanology, and other Earth sciences.