Figure 8 shows the visible half of the celestial sphere at observation site .
Here, is the local horizon, and , , , and are
the north, east, south, and west compass points, respectively. The plane ,
which passes through the north and south compass points, as well as the zenith,
is known as the local *meridian*. The meridian is perpendicular
to the horizon. The north celestial pole lies in the meridian plane, and
is elevated an angular distance above the north compass point--see Figs. 7 and 8. Here,
is the terrestrial *latitude* of observation site . It is helpful to
define three, right-handed, mutually perpendicular, local unit vectors: , , and .
Here,
is directed toward the east compass point, toward the north compass point, and toward the zenith--see Fig. 8.

Figure 9 shows the meridian plane at . Let the line lie
in this plane such that it is perpendicular to the celestial axis, . Moreover, let
lie in the visible hemisphere. It is helpful to define the unit vector which
is directed toward , as shown in the diagram. It is easily seen that

Figure 10 shows the celestial equator viewed from observation site . Here, is
the right ascension of the celestial objects culminating (*i.e.*, reaching
their highest altitude in the sky) on the meridian at the time of observation. Incidentally, it is
easily demonstrated that all objects culminating on the meridian at
any instant in time have the *same* right ascension. Note that the angle
increases uniformly in time, at the rate of a (sidereal) hour, due to the diurnal motion of the celestial
sphere. It can be seen from the diagram that

Thus, from Eqs. (17) and (18),

Similarly, from Eqs. (6) and (7),