Not a physicist here but something has been puzzling me for a while. As I understand gravity in General Relativity, it bends the space time as this Picture. Now this is all nice and elegant if I look at the problem from the plane of trajectory perspective.
My real question is this. A planet is a three dimensional object. So the space "bending" has to be done in a three dimensional ( or more) way such that every time I limit myself to a plane perspective passing through the center of the planet. I get the original linked picture.
So I guess my question is, how is space being really bent? Is there a way to bend it in 3D that I am not aware of? or is there an extra invisible dimension being involved?