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How to draw edges on a sphere to make parts that fit into each other

I am trying to make sphere shaped designs with moving parts like spaceship doors & windows for 3d printing. However, the doors/windows don't always follow the edges on the UV sphere.

Is there a way to "draw" edges on the surface of the sphere that I can use to cut certain shapes out of it? The best example I can think of are the classic flying saucer spaceships with the lowering door in older movies.