The moon rotates every 29.5 days, therefore each lunar day lasts approximately four weeks. This can create problems in calculating times for observance of mitzvot.
Many Jewish observances are time bound and Earth bound.
A popular joke, from the days of the first space missions, describes the space voyage of the first Orthodox Jewish astronaut. When he returns to Earth he is asked about his experience. There is also a problem with determining the start of Sabbath and festivals. Rabbi David Slush tackled the question of calculating the time for prayers. He recommended that the Shema be recited when the astronaut goes to sleep and when he wakes up, regardless of what time it is in the zone of Earth he is flying over.