The Propagation of Light Pollution in Diffusely Urbanised Areas
  The knowledge of the contribution $b_d(d)$ to the artificial sky luminance in a given point of the sky of a site produced by the sources beyond a given distance $d$ from it is important to understand the behaviour of light pollution in diffusely urbanized areas and to estimate which fraction of the artificial luminance would be regulated by norms or laws limiting the light wasted upward within protection areas of given radii.   I studied the behaviour of $b_d(d)$ constructing a model for the propagation of the light pollution based on the modelling technique introduced by Garstang which allows to calculate the contribution to the artificial luminance in a given point of the sky of a site of given altitude above sea level, produced by a source of given emission and geographic position. I obtained $b_d(d)$ integrating the contribution to the artificial luminance from every source situated at a distance greater than $d$. I also presented an analitical expression for $b_d(d)$ depending mainly from one parameter, a core radius, well reproducing model's results.   In this paper I present the results for $b_d(d)$ at some Italian Astronomical Observatories. In a diffusely urbanised territory the artificial sky luminance produced by sources located at large distances from the site is not negligible due at the additive character of light pollution and its propagation at large distances. Only when the core radius is small, e.g. for sites in the inner outskirts of a city, the sky luminance from sources beyond few kilometers is negligible. The radii of protection zones around Observatories needs to be large in order that prescriptions limiting upward light be really effective. 
P. Cinzano (Dipartimento di Astronomia, Padova, Italy)