USNO Circular 179 - U.S. Naval Observatory

66 MODELING THE EARTH’S ROTATION
although this equation is not needed in hour angle computations; it is given here only for completeness.
The common notion of hour angle can be expressed more precisely using concepts introduced
in Chapters 5 and 6. The local hour angle of an object is the angle between two planes: the plane
containing the geocenter, the CIP, and the observer; and the plane containing the geocenter, the
CIP, and the object. Hour angle increases with time and is positive when the object is west of
the observer as viewed from the geocenter. The two planes define meridians on the celestial sphere
that meet at the CIP. From the point of view of the observer, the CIP is not, in general, exactly
at the geodetic north point, which is the direction toward the ITRS z-axis. The azimuths of the
two directions differ by as much as
x 2 p + y 2 p/ cos φ ITRS , depending on time of day. This difference
is small (usually