Relying on the students' cultural background to teach mathematics may be a strong incitement for the learning process. This background can include artistic creations, items from the news, among others. Because of the strong presence of space related news (in particular the almost simultaneous launching of three spacecrafts towards Mars), we present activities in a technology-rich environment, using both a Dynamic Geometry System and a Computer Algebra System. We start from a simplified model of planetary orbits and building new knowledge on plane curves. Interesting byproducts are the discovery of the strong influence of changing numerical approximations, non-trivial aspects of the study of periodicity, the plotting of interesting curves and their connections with existing pieces of visual art, including architecture and mandalas. The educative aspect of these activities is also discussed and is presented from the point of view of STEAM Education.