Modern planetariums are digital immersive facilities that promise new teaching opportunities beyond their historic limitations as analog instructional media in astronomy education. We investigated the use of a planetarium as a teaching and learning space by analyzing student responses gathered from a cohort of university students during two separate planetarium visits which constituted part of their introductory astronomy course. An instrument was first developed to probe how the students responded to the overall planetarium experience and how they engaged with the educational content. In the second student visit, show content was specifically designed by us and the instrument was modified based on the results of the first visit. Individual student responses were coded for higher-level categories and concepts. From these concepts we developed a localized mid-level model of student engagement. This led to the notion of a "spectrum of attentiveness" that strongly influences how students engage with relevant educational content.