I know that the title sounds like a sequel to a TV show (Lost in space). But based on a statement in this article :
The Rabbis therefore rule that a person should continue to follow the time from the place from which he departed. Based on this, it is possible that different people in a space station or on the moon who came from different places will be observing different times.
If a Jew was born in space (station), he has never "departed" from Earth. What times does he follow, or does he follow his Mom's minhag? Let's assume that Dad is still on Earth and Mom travelled to the space station while she was pregnant (If any of these factors would matter in answering the question?)