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
Pole.

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:

In any case, when you go back to the "Motion on a
Globe" explanation, keep in mind that motion at constant θ results
in a great circle, but motion at constant φ only gives you a great circle
if you're at φ=90°. At any other value of φ, a free-flying
object sent due "East" or "West" will soon change its value of φ.
Geometrically speaking, a line at constant φ other than at the equator is
not a "straight line" (or geodesic (Wikipedia link)) in
the sense of being the shortest distance between two points. And free-flying
objects will try to move along the shortest possible path.