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, then we have:
right ascension of X = arcB
hour angle of X = ∠ZPX = arc AB.
But
A = B + BA
hence,
hour angle of X + right ascension of X = local sidereal time
or
HAX + RAX = LST. (1)
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 (1) are known, the third can be calculated. We will consider the implications of this later when we look at sidereal time in more detail.

Figure1. Ecliptic coordinates.