Physicists have conclusively proven that if a spaceship leaves Earth and travels fast enough, then turns around and comes back, a person in the spaceship experiences a much shorter time than people on Earth - a few days for the astronaut could be years on Earth.
The usual answer for people who are travelling outside zones where normal z'manim make sense (more locally in space or even to the Arctic Circle) is to use the times from where they set off from. However, this probably doesn't make much sense here as they could be in a situation where they don't have sufficient time do daven before the next z'man arrives, and Shabbos could be eg. every few minutes!
Is there any source for Halachic reasoning as to what such a traveller should do?