We have made differential radial velocity measurements of the star alpha Cen A using two spectrographs, UVES and UCLES, both with iodine absorption cells for wavelength referencing. Stellar oscillations are clearly visible in the time series. After removing jumps and slow trends in the data, we show that the precision of the velocity measurements per minute of observing time is 0.42 m/s for UVES and 1.0 m/s for UCLES, while the noise level in the Fourier spectrum of the combined data is 1.9 cm/s. As such, these observations represent the most precise velocities ever measured on any star apart from the Sun.
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