Verified answer

Well, ..., you don't need a special printing press for this but you do need to watch the YouTube videos below. You can do this very easily with materials that you probably already have around the house or at your local craft store. If you'll follow the processes and ideas outlined in the video's, I'm sure that you'll be able to make a fantastic solar system popup book.

You will probably need very elaborate materials and a printing press - I doubt there are any "cut out" diagram sheets on the internet for those.