The Essential Properties of a Coordinate System

1. The physical basis (Condition #1) for this illustration has been left here as an open question.
2. The FGC (Condition #2) has been constructed in a generic way, i.e., as a simple diametric cut through the sphere and oriented more or less horizontally for our convenience.
3. How is the "Pole" (Condition #3) found? Generally speaking, in order to make our coordinate systems oriented in a "right-handed" way, wrapping the fingers of one's right-hand in the direction of the rotary motion of the system (a feature of most celestial systems but not necessarily of industrial applications) forces the Pole to be in the direction of the right-hand thumb pointing in the "thumbs up" position. Yet another example of mankind's inhumanity to left-handed people.
4. The secondary great circle (s.g.c.) of interest (Condition #4), often called a "meridian," runs through both poles, as well as Point "X" and Point "M"; the latter point is defined as at the intersection of the s.g.c. and the FGC.
5. The "zero" positions (Condition #5) are found along the FGC.
6. The coordinates (f,g) (Condition #6) of the point "X" on the spherical surface are shown increasing from their respective "zero" positions:
   • f increases towards the Pole from the FGC;
   • g increases usually clockwise (CW) from its origin, at Point "C," on the FGC.