  Spectrograph aboard the GAIA satellite operates in the near-IR, in the 8490--
8740 \AA window accessible also from the ground. The most important parameter
yet to be determined is the spectral resolution. Realistic estimates of the
zodiacal light background are obtained and a total of $2\times 10^5$
correlation runs are used to study the accuracy of radial velocity measured by
the spectrograph as a function of resolution, magnitude of the target, its
spectral type and luminosity class. Accuracy better than 2 km/s is achievable
for bright stars if a high enough dispersion is chosen. Radial velocity error
of 5 km/s is at $V=17.5$ for Cepheids and at 17.7 for horizontal branch stars.
Even for very faint objects, with spectra dominated by background and readout
noise, the optimal dispersion is still in the 0.25 / 0.75 \AA/pix range. This
is also true for complicated cases such as spectroscopic binaries or if
information other than radial velocity, i.e. abundances of individual elements
or stellar rotation velocity, is sought after. The results can be scaled to
assess performance of future ground based instruments.
