Introduction: We report an investigation on collaboration practices in research papers published in the most prestigious English-medium astrophysics journals. Method: We propose an evaluation method based on three numerical indicators to study and compare, in absolute terms, three different types of collaboration (international, national and local) and authors' mobility on the basis of co-authorship. Analysis: We analysed 300 randomly selected research papers in three different time periods and used the student's t-test to determine whether the paired two-sample differences observed were statistically significant or not. Results: International collaboration is more common than national and local collaboration. International, national and local authors' mobility and intra-national collaboration do not seriously affect the indicators of the principal levels of collaboration. International collaboration and authors' mobility are more relevant for authors publishing in European journals, whereas national and intra-national collaboration and national mobility are more important for authors publishing in US journals. Conclusions: We explain the observed differences and patterns in terms of the specific scope of each journal and the socio-economic and political situation in both geographic contexts (Europe and the USA). Our study provides a global picture of collaboration practices in astrophysics and its possible application to many other sciences and fields would undoubtedly help bring into focus the really big issues for overall research management and policy.