I apologize for how late this is. NASA is an amazing place. I live in Houston for 3 years and, as you can imagine, the LOVE of the study of Space there is really ALIVE. The way you describe research on curiosity is so valuable for students to feel exctied about a subject they have interest in. Thinking about people like JFK and Bill Gates and Steve Jobs...how they would create a goal with their engineers, scientist and mathemeticians, I love this topic. I think it has great value for students undertanding that while some folks may think the UNKNOWN is not worth knowing, where would future wisdom and growth come from. Such an important thing to instill in our students and help them EMBRACE and work on developng their ideas!
I think finding how math problems relating to space exploration and creating word problems on this would be fun!