If a Cohen astronaut orbits the earth in a spacecraft, would he have a problem of ohel zorek?
No, there would be no problem.
Poskim discuss the question of an ohel zaruk with regard to an airplane, and explain that the airplane does not have a problem of ohel zaruk, because it does not have any attachment with the ground, unlike an ohel on top of an animal, and so on.
See Shut Eretz Tzvi 1:93; see also Rav Chaim Brisker, Tumas Mes 11:5.
Of course, a spacecraft has even less connection with earth than a regular airplane.
So if you’re a Cohen preparing for takeoff, you needn’t have any tumah-related fears!