Astrology meets a large success in our societies, from the private to the political sphere as well as in the media, in spite of the demonstrated inaccuracy of its psychological as well as operational predictions. We analyse here the relations between astrology and astronomy, as well as the criticisms opposed by the latter to the former. We show that most of these criticisms are weak. Much stronger ones emerge from the analysis of the astrological practice compared to the scientific method, leading us to conclude to the non-scientificity of astrology. Then we return to the success of astrology, and from its analysis we propose a renewed (and prophylactic) rôle for astronomy in society.