Extragalactic Source Counts and Contributions to the Anisotropies of the Cosmic Microwave Background. Predictions for the Planck Surveyor mission

We present predictions for the counts of extragalactic sources, the contributions to fluctuations and their spatial power spectrum in each channel foreseen for the Planck Surveyor (formerly COBRAS/SAMBA) mission. The contribution to fluctuations due to clustering of both radio and far--IR sources is found to be generally small in comparison with the Poisson term; however the relative importance of the clustering contribution increases and may eventually become dominant if sources are identified and subtracted down to faint flux limits. The central Planck frequency bands are expected to be ``clean'': at high galactic latitude (|b|>20), where the reduced galactic noise does not prevent the detection of the extragalactic signal, only a tiny fraction of pixels is found to be contaminated by discrete extragalactic sources. Moreover, removal of contaminating signals is eased by the substantial difference between their power spectrum and that of primordial fluctuations.