This is not meant to be a "Purim Torah" question.
The concept of Rosh Hodesh is based on the orbit of the moon around Earth. But, with the proposal of sending people to live permanently on Mars, I assume that it won't be long before they have people live permanently on the moon.
So, if someone did live permanently on the moon. Things are relative. From that person's viewpoint, Earth looks like the moon's "moon". So, it would like Earth has a "molad". Would you have to observe Rosh Hodesh at the same time and in the same manner as if you would living on Earth?
Similarly, I guess you would call it "Kiddush Ha'Aretz" (or "Adamah?") - would you have to recite that each month?