If the Death Star had a gravitational pull like a real moon would have had, then logically it should have looked like this;
LOL @ picture. I can just imagine seeing that in the movie.
Anyways, about gravity, I’ve always been aware that they have some kind of gravity control in the floors, not sure where I read it, was it from the cross sections book or where. That’s why there is gravity on ships, like Falcon, star destroyers etc. I don’t think the gravity is at DS’s core, it would make no sense when we see what we see. Also if they were in the floors, you could flip the floors the way you want, so you can have the DS gunners shooting X-Wings etc.
I’m sure the EU has some clever explanation/excuse for it all, my point is simply that it’s not important to the overall film(s).