Carl Zeiss is the scientest of Jena in Thuringia famous for his measuring and optical instruments. He's also the man Stuttgart's planetarium is named after. If you are a fan of astronomy, and have a few hours to spare, then it is one of the best places to view the stars in Germany. It also has the occasional special event, such as the local philharmonic orchestra playing while you watch the stars, or a segment on the mysteries of the Dogon star. You'll need to speak German to make sense of the latter.
Its opening times are a little non-standard, but you can check this page for more information. It's in German, but you can work out what it is saying if you remember that Dienstag is Tuesday, and all the other days listed follow sequentially in the list. Entry is 5 euros for adults, and 3 for children.
The Planetarium was built between 1975 and 1977 by the architect Beck Erlang. There are several programms which alter every 2 months.