Description of Coordinate Systems

Each coordinate system we describe in the following is defined by the orientation of its three right handed cartesian axes in euclidean space and the position of its origin, relative to some other system. The +Z-axis always defines the polar axis of the respective spherical coordinates: latitudes are counted from the XY-plane (polar axis $90^\circ$), co-latitudes from the polar axis, longitudes are counted from the +X-axis (prime meridian) clockwise (left handed, +Y-axis $-90^\circ$) or counter-clockwise (right handed, +Y-axis $90^\circ$) as specified.