A few days ago, Kim Andrew Elliot mentioned the 30th anniversary of the journey of Vladimír Remek into space. Remek made history in 1978 as the first person to travel into space who wasn’t from the United States or the Soviet Union (he was born in Czechoslovakia). According to the story, he listened to shortwave broadcasts from all over the world while in space and heard his name mentioned in many languages.
I was amused to read this because I remembered the time a few years ago when someone explained to me in great detail why listening to a shortwave broadcast in space would be impossible. His explanation made sense and he seemed quite confident in his reasoning. Unfortunately for him, apparently not only is it possible, but it had already been done years before he made his explanation!
In 2004, Vladimír Remek was elected a Member of the European Parliament. In an interview on the European Parliament site, he describes his path to space and mentions his space shortwave listening. So apparently if you ever travel to space, you can listen to some shortwave broadcasts while you are there. But considering all of the shortwave stations that have shut down recently, your problem might be finding a broadcast at all!