The Rosetta spacecraft has been successfully launched on 2nd March 2004 to its new target comet 67 P/Churyumov-Gerasimenko. The science objectives of the Rosetta Radio Science Investigations (RSI) experiment address fundamental aspects of cometary physics such as the mass and bulk density of the nucleus, its gravity field, its interplanetary orbit perturbed by nongravitational forces, its size and shape, its internal structure, the composition and roughness of the nucleus surface, the abundance of large dust grains, the plasma content in the coma and the combined dust and gas mass flux. The masses of two asteroids, Steins and Lutetia, shall be determined during flybys in 2008 and 2010, respectively. Secondary objectives are the radio sounding of the solar corona during the superior conjunctions of the spacecraft with the Sun during the cruise phase. The radio carrier links of the spacecraft Telemetry, Tracking and Command (TT&C) subsystem between the orbiter and the Earth will be used for these investigations. An Ultrastable oscillator (USO) connected to both transponders of the radio subsystem serves as a stable frequency reference source for both radio downlinks at X-band (8.4 GHz) and S-band (2.3 GHz) in the one-way mode. The simultaneous and coherent dual-frequency downlinks via the High Gain Antenna (HGA) permit separation of contributions from the classical Doppler shift and the dispersive media effects caused by the motion of the spacecraft with respect to the Earth and the propagation of the signals through the dispersive media, respectively. The investigation relies on the observation of the phase, amplitude, polarization and propagation times of radio signals transmitted from the spacecraft and received with ground station antennas on Earth. The radio signals are affected by the medium through which the signals propagate (atmospheres, ionospheres, interplanetary medium, solar corona), by the gravitational influence of the planet on the spacecraft and finally by the performance of the various systems involved both on the spacecraft and on ground.