Astronomy: State of the Art is a massive, open, online class (MOOC) offered through Udemy by an instructional team at the University of Arizona. With nearly 24,000 enrolled as of early 2015, it is the largest astronomy MOOC available. The astronomical numbers enrolled do not translate into a similar level of engagement. The content consists of 14 hours of video lecture, nearly 1,000 Powerpoint slides, 250 pages of background readings, and 20 podcast interviews with leading researchers. Perhaps in part because of the large amount of course content, the overall completion rate is low, about 3%. However, this number was four times higher for an early cohort of learners who were selected to have a prior interest in astronomy and who took the class in synchronous mode, with new content being added every week. Completion correlates with engagement as measured by posts to the online discussion board. For a subset of learners, social media like Facebook and Twitter provide an additional, important mode of engagement. For the asynchronous learners who have continuously enrolled for the past 15 months, those who complete the course do so quickly, with few persisting longer than two months. The availability of a free completion certificate had no impact on completion rates when it was added midway through the period of data analyzed in this paper. This experiment informs a new offering of an enhanced version of this MOOC via Coursera, along with a co-convened "flipped" introductory astronomy class at the University of Arizona, where the video lectures will be online and class time will be used exclusively for small group labs and hands-on activities. Despite their typically low completion rates, MOOCs have the potential to add significantly to public engagement with science, and they attract a worldwide audience.