The Gaia mission is designed as a Galaxy explorer, and will measure simultaneously, in a survey mode, the five or six phase space parameters of all stars brighter than 20th magnitude, as well as providing a description of their astrophysical characteristics. These measurements are obtained by combining an astrometric instrument with micro-arcsecond capabilities, a photometric system giving the magnitudes and colours in 15 bands and a medium resolution spectrograph named the Radial Velocity Spectrometer (RVS). The latter instrument will produce spectra in the 848 to 874 nm wavelength range, with a resolving power R = 11 500, from which radial velocities, rotational velocities, atmospheric parameters and abundances can be derived. A companion paper (Katz et al. 2004) presents the characteristics of the RVS and its performance. This paper details the outstanding scientific impact of this important part of the Gaia satellite on some key open questions in present day astrophysics. The unbiased and simultaneous acquisition of multi-epoch radial velocities and individual abundances of key elements in parallel with the astrometric parameters is essential for the determination of the dynamical state and formation history of our Galaxy. Moreover, for stars brighter than V=15, the resolving power of the RVS will give information about most of the effects which influence the position of a star in the Hertzsprung-Russell diagram, placing unprecedented constraints on the age, internal structure and evolution of stars of all types. Finally, the RVS multi-epoch observations are ideally suited to the identification, classification and characterisation of the many types of double, multiple and variable stars.
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