>By that reasoning, astrology is a science, because it can be studied using the scientific method.

exactly, one can do pure scientific study of correlation between that star position and people's lives and most probably would find zero correlation - it would be a valid (though practically useless given current state of science in related areas) scientific study in the domain of astrology. That domain happens to be full of non-scientific results and statements while has no useful non-trivial scientific results known. Thus people label the domain as 'non-science'. Economics has a lot of both.