POSITIONS ON A SPHERE
The location of an exact position on the surface of a sphere can be expressed in a variety of ways. The particular method used in navigation and astronomy makes use of two coordinates. The angle between the polar axis and the position, and an angle measurement around the polar axis from a meridian reference line which is arbitrarily established. The reference meridian is a great circle through both poles. Referring to Figure 9, the position A is labeled by an angle (called the Polar Distance) between the polar axis and the position, and an angle (called the Azimuth Angle) measured either clockwise or counter-clockwise from the reference line. The polar angle can be measured directly from the cursor scale on the spanner. The azimuthal angle between the reference meridian and the spanner cursor can be measured direclty from the rosetta on the spanner, or between the intersection at the equator of the reference line and the spanner cursor.
For positions in the southern hemisphere, polar distance is measured from the south pole and labeled with an S.
The same types of measurements are used to determine positions with respect to the position of the observer. Referring to Figure 10, the spanner is positioned with the spanner rosetta centered over the observer's position, and the spanner cursor line lying on position A. The angle measured between the observer's position and position A is called the ZENITH DISTANCE. The observer's location and the center of the sphere define the ZENITH DIRECTION. The zenith direction is an imaginary line from the center of the sphere through the observation point, and extending above the observer.
Azimuthal angle at the observer's position is called BEARING and is usually measured with respect to the meridian through the observer's position and the poles.