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It is convenient to specify the positions of celestial objects in the sky, when viewed from
a particular observation site, , on the earth's surface, using a pair of angular coordinates, and ,
which are measured with respect to the local horizon. Let denote
a celestial object, and the projection of the line onto the
horizontal plane, see Fig. 11. The coordinate , which
is known as altitude, is the angle subtended between and
. Objects above the horizon have positive altitudes, whereas
objects below the horizon have negative altitudes. The
zenith has altitude , and the horizon altitude . The coordinate ,
which is known as azimuth, is the angle subtended between
and . Azimuth increases from the north towards the east. Thus, the
north, east, south, and west compass points have azimuths of
, , , and , respectively.
Note that the basis vectors in the horizontal coordinate system are ,
, and , whereas the corresponding basis vectors in the
celestial coordinate system are , , and see Figs. 3 and 8. By analogy with Eqs. (1)(3), we can write
where is a unit vector directed from to .
Hence, it follows from Eqs. (1), and (22)(23), that
These expressions allow us to calculate the altitude and azimuth of a
celestial object of declination and right ascension
which is viewed from an observation site on the earth's surface of terrestrial latitude at an instant in time
when celestial objects of right ascension are culminating at the meridian.
According to Eqs. (8), and (25)(26),
the altitude and azimuth of a similarly viewed point on the ecliptic (i.e., ) of ecliptic
longitude are given by
Figure 11:
Horizontal coordinates. is a celestial object, and
its projection onto the horizontal plane, .

Next: Meridian Transits
Up: Spherical Astronomy
Previous: Local Horizon and Meridian
Richard Fitzpatrick
20100721