Before watching it, I was preparing to describe here a bit of Professor Hawking's crossing of paths with the troupe, but to their great credit (and understandably) they themselves make that clear in the video. Though having a bit of explanation might add to the perspective of things.
In the recent Monty Python reunion concerts in London, the show includes a filmed sketch in which Stephen Hawking appears. They don't include the entire sketch in the video, but enough to appreciate it. (Basically, the premise is a very real professor -- I believe -- is standing on a riverbank outside his university and lecturing quite pompously. And...well, let's just say that it's far too pompous for Professor Hawking's liking.) And then when they return back to the live show at London's 02 auditorium, it turns out that Stephen Hawking is there in attendance, much to the roaring approval of the enthusiastic crowd.)
Apparently, the Monty Python folks imposed about Professor Hawking to sing "Galaxy Song," a number which was originally done for the opening of the 1983 film, Monty Python's Meaning of Life. That movie holds a place near-and-dear to my heart since I was in the Universal Studios P.R. Department at the time, when we released the film. And as part of a promotional event for a screening, I moderated a Q&A session with most of the Pythons -- Terry Jones, Eric Idle, Graham Chapman and Terry Gilliam. Alas, Michael Palin (my fave) and John Cleese were not in attendance. And alas, as well, I don't remember much about it, since, as you can probably appreciate, my head was exploding too much at the time. I do remember everyone being reasonably personable, but Terry Jones as being particularly nice.
I think it helps to watch this twice. The first time, I suspect most people's attention will be divided between the singing and the entertaining visuals. The second time, you can focus more on just the singing, which is quite a treat, without any distractions.
Here then is the tune, and the vocal stylings of Professor Stephen Hawking.