Radial velocities (RV) measured from near-infrared (NIR) spectra are a potentially excellent tool to search for extrasolar planets around cool or active stars. High resolution infrared (IR) spectrographs now available are reaching the high precision of visible instruments, with a constant improvement over time. GIANO is an infrared echelle spectrograph at the Telescopio Nazionale Galileo (TNG) and it is a powerful tool to provide high resolution spectra for accurate RV measurements of exoplanets and for chemical and dynamical studies of stellar or extragalactic objects. No other high spectral resolution IR instrument has GIANOs capability to cover the entire NIR wavelength range (0.95-2.45 micron) in a single exposure. In this paper we describe the ensemble of procedures that we have developed to measure high precision RVs on GIANO spectra acquired during the Science Verification (SV) run, using the telluric lines as wavelength reference. We used the Cross Correlation Function (CCF) method to determine the velocity for both the star and the telluric lines. For this purpose, we constructed two suitable digital masks that include about 2000 stellar lines, and a similar number of telluric lines. The method is applied to various targets with different spectral type, from K2V to M8 stars. We reached different precisions mainly depending on the H -magnitudes: for H ~ 5 we obtain an rms scatter of ~ 10 m s-1, while for H ~ 9 the standard deviation increases to ~ 50 - 80 m s-1. The corresponding theoretical error expectations are ~4 m s-1 and 30 m s-1, respectively. Finally we provide the RVs measured with our procedure for the targets observed during GIANO Science Verification.
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