I'm working on an SF story that takes place in a future in which there are spaceships and space travel. Nothing unique there. I want the characters to be in the military and on a spaceship, and I'm trying to figure out what that would look like in terms of the military. In other words, what branch of the military would have/deploy spaceships? Would it be more than one branch or a new branch altogether? Is it really likely that a there is a new kind of military that polices the entire Earth but does not belong to any one country on it? How would the military in space be related to the armed forces on the ground? And so on.
Of course, these aren't questions that have definitive answers. But I was wondering what someone with military experience thought about that kind of scenario. The books and shows I've seen with military themes don't really talk about how they fit in with the way our military works, or they just make a space-faring military "universal," as if it belongs to the U.N. They also seem to use naval ranking which I find odd (as opposed to Air Force, which seems the most similar to flying a space ship).