The way we interact with the Internet would have to change though due the extra delays involved in communication between planets.
A lunar base would have a delay of about 2.5 seconds, so could probably just connect direct to the Internet on Earth via a few gateways located on the Earth (possible just a simple SOCKS proxies with a high value on the TCP Timeouts on it's lunar side). It would be slow, so you'd want to include quite a bit of caching for data on both sides that doesn't change.
Once you start talking about other planets though your delays would start to become unusable for interactive operations (between 5 and 20 minutes for Mars), so at that point you'd have to start thinking about using more asynchronous methods of communication (e.g. send an email rather than use a chat session).
I have to admit that part of me loves the idea of using a variation of FidoNet for interplanetary communication :)
I'm shocked that Google is behind this. I would have thought the ROI would be a hard sell.
It neat to hear how involved they are in space.
Setting that up would be challenging. You have to have each network node aware of locations of the rest of the network.
Thanks so much for sharing that. I'm sad it's only got 40 likes.