I guess you would have to use an Earth-based remote desktop.
I guess you would have to use an Earth-based remote desktop.
For browsing the web, they would send a message requesting a page, and get back the messages for the page in 30 minutes. They would probably send a request for whole site instead of round-trips for links.
This means that interactive JavaScript sites would never work. There would need to be way to download app or web app that could send messages to update state. Or way to install local server that can sync with Earth.
Getting website articles and other media via rss feeds would be easiest. Email and usenet style nntp, also.
There's been work done on protocols optimized for inter-planetary networks, taking into round trip times when it comes to retransmissions and windowing, etc. Gateways can be setup between those protocols and earth's tcp internet.
But every communication back and forth still takes many minutes. Interactive websites would take at least one round trip minutes for every request, every form submission, every javascript call to a back-end server, etc. Remote desktop solutions would encounter this same problem, too.
At the moment the fastest link to Mars is about 6 megabits per second. Presumably that could be scaled up quite a bit, but I assume bandwidth will be a consideration for a while, too.
Early on it will make sense to bring a lot of your own entertainment media and reference materials via thumb drive or other storage media, to have instant access and save bandwidth for other things.
Counterstrike or zoom meetings? Not so much.
the "internet" is just a network of computers. "sync up the two" would involve replicating the servers and coming up with some sort of consensus protocol. Needless to say, that's non-trivial to implement and needs to be done for each site individually. If there was a martian colony it might be economically feasible for some sites to do this, but if it's just a few astronauts the most feasible way of implementing internet browsing would be something like archive.today, where you send a url to some server on earth, the server runs a headless browser and takes a screenshot, and sends the captured contents back to mars/spacecraft.
Robust caching would help but still be nothing like what we experience on Earth (particularly the interactive portions of the web like, say, HN).