During the early Cold War, outer space became a politically contested space, and changes in its spatial perception were related to political and ideological controversies. The article highlights the specific relevance of Euclidean geometry in representations of outer space. Focusing on illustrations and expositions in both postwar German States, it argues that shifts within the spatial imagination and representation of space corresponded with the first satellite missions and condensed debates about the future of technology and the moral legacies of the Second World War. In October 1957, Sputnik I, the first artificial satellite to orbit the Earth and a Soviet construction, urged engineers, scientists, and illustrators to find new ways of depicting and communicating the spaces of outer space to the public and to each other. For decades, space fiction had implicitly stifled theories on the relativity of space and time by hinting at traditional motifs of conquest through machines. Early spaceflight, however, was not about immediate flights to other planets, but about the orbit, a space without a traditional place, yet imagined as being of paramount importance for strategic superiority. Driven by political tensions and drawing on representations established in physics and astronomy, the first satellite projects were designed and explained as missions to places that needed to be defined and controlled because they were strange and new.