This entry has been adapted from a short answer I gave on Quora.com
On Earth? Yes, of course.
On the ISS? Not really. The space agencies have thought of that.
The International Space Station runs on Coordinated Universal Time (UTC) which is just GMT +00:00 (or as we call it in Britain, “the time”). There are a few reasons for this, but one of them being it’s a nice balance being roughly in the middle of the two main ISS control centers, Houston (GMT - 05:00) and Moscow, (GMT + 03:00). Coincidentally, this is very convenient for the EuroCOMMS situated in Cologne, Germany (GMT + 01:00) who are tasked with monitoring the European module Columbus laboratory and the European astronaut on board.
Around 10–14 days before launch, while in Baikonur, Kazakhstan, the prime and backup crews go into quarantine in order to prevent the spread of any illnesses to the station. During this quarantine all visitation is restricted subject to the flight surgeon’s approval.
During quarantine the crew stays mainly indoors and begins to operate on UTC in order to mitigate jet lag when they do finally make it to the ISS.
However, even with no jet lag going to space is pretty rough physiologically.
If they are lucky (i.e. orbital mechanics permits a short rendezvous time of around 6 hours rather than the 2 days that is often required), they routinely arrive at station about 16+ hours after waking up. This is due to their packed launch day schedule which includes breakfast, last Earthly shower, enema (yes, this is true. Astronauts can request an enema the 'Russian way' or the 'American way'!), suiting up, leak checks, press conference, family goodbyes, peeing on a tire, signing a door, getting in a space capsule, staying in said capsule for several hours, blasting off from earth, orbiting the planet, docking with a space station, checking the seal, moving into their new home and finally one more press conference once on board.
This, coupled with Space Adaption Syndrome makes for a pretty rough, although probably very rewarding, first few days in space!
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