||We extend the method introduced by Cinzano et al. (2000a) to map the artificial sky brightness in large territories from DMSP satellite data, in order to map the naked eye star visibility and telescopic limiting magnitudes. For these purposes we take into account the altitude of each land area from GTOPO30 world elevation data, the natural sky brightness in the chosen sky direction, based on Garstang modelling, the eye capability with naked eye or a telescope, based on the Schaefer (1990) and Garstang (2000b) approach, and the stellar extinction in the visual photometric band. For near zenith sky directions we also take into account screening by terrain elevation. Maps of naked eye star visibility and telescopic limiting magnitudes are useful to quantify the capability of the population to perceive our Universe, to evaluate the future evolution, to make cross correlations with statistical parameters and to recognize areas where astronomical observations or popularisation can still acceptably be made. We present, as an application, maps of naked eye star visibility and total sky brightness in V band in Europe at the zenith with a resolution of approximately 1 km.