Astronomy Principles and Practice Fourth Edition.pdf

78 The celestial sphere: coordinate systems
Figure 8.18. The celestial sphere illustrating local sidereal time.
Sun’s setting the position will mean a stake-shift of the order of 2 m. This demonstrates the sensitivity
of the method and the ingenuity of this ancient culture.
8.13 Sidereal time
Right ascension, together with declination, forms a coordinate system for stellar positions useful in
constructing star catalogues, in contrast to the alt-azimuth and equatorial systems where one or both
coordinates change rapidly with time.
The First Point of Aries, , being a point on the stellar background, will rotate with the heavens
like a star, transiting and rising and setting. We can, therefore, give a precise meaning to the phrase,
‘the hour angle of (HA)’. It is the angle which the meridian through makes with the observer’s
meridian, ZP in figure 8.18. It is also called the local sidereal time (LST). Hence,
HA = LST.
If X is the position of a star, its meridian PX meeting the equator at the point B,thenwehave:
right ascension of X = arcB
hour angle of X = ZPX = arc AB.
But
hence,
or
A = B + BA
hour angle of X + right ascension of X = local sidereal time
HAX + RAX = LST. (8.7)
This is an important relationship for X can be any celestial object—star, Sun, Moon, planet, even
an artificial satellite or spacecraft. If any two of the three quantities in equation (8.7) are known, the
third can be calculated. We will consider the implications of this later when we look at sidereal time in
more detail.