Some of you may be thinking, "If we're ignoring the spin of the globe, how
can we even have a North and South? Aren't those defined by the axis
of rotation?" Well, it's easiest to define it that way, sure. But you don't
need a spinning sphere in order to use a coordinate system that has a North
Spherical Cartesian Coordinates (Wikipedia link) define position with three variables: ρ (radius from center), φ (latitude) and θ (longitude). The angle φ is defined as starting at some arbitrary direction, which is usually drawn as "up" on the page. Or, to relate it to a planet, it's measured as degrees down from the North Pole.
When you have a spinning planet, it's convenient to use the axis of rotation to define the starting point for φ. However, the starting point for θ is totally arbitrary, even on a spinning sphere. By convention, on Earth we say θ=0° at the Prime Meridian (Wikipedia link), but it could be anywhere.
On a non-spinning sphere, the starting point for φ is just as arbitrary as the starting point for θ. Once we've laid out our coordinates, moving in each cardinal direction is defined as follows: