Equatorial Coordinate System :
Because the altitude and azimuth of a star are constantly changing, it is not possible to use the horizontal coordinate system in a catalog of positions. A more convenient coordinate system for cataloging purposes is one based on the celestial equator and the celestial poles and defined in a similar manner to latitude and longitude on the surface of the Earth. In this system, known as the equatorial coordinate system, the analog of latitude is the declination, δ. The declination of a star is its angular distance in degrees measured from the celestial equator along the meridian through the star. It is measured north and south of the celestial equator and ranges from 0° at the celestial equator to 90° at the celestial poles, being taken to be positive when north of the celestial equator and negative when south. In the figure below, the declination of the star X is given by the angle between Y and X.
The analog of longitude in the equatorial system is the hour angle, H (you may also see the symbol HA used). Defining the observer's meridian as the arc of the great circle which passes from the north celestial pole through the zenith to the south celestial pole, the hour angle of a star is measured from the observer's meridian westwards (for both northern and southern hemisphere observers) to the meridian through the star (from 0° to 360°). Because of the rotation of the Earth, hour angle increases uniformly with time, going from 0° to 360° in 24 hours. The hour angle of a particular object is therefore a measure of the time since it crossed the observer's meridian - hence the name. For this reason it is often measured in hours, minutes and seconds of time rather than in angular measure (just like longitude). In figure above, the hour angle of the star X is given by the angle Z-NCP-X. Note that all stars attain their maximum altitude above the horizon when they transit (or attain upper culmination on, in the case of circumpolar stars) the observers meridian.
The declination of a star does not change with time. The hour angle does, and hence it is not a suitable coordinate for a catalogue. This problem is overcome in a manner analogous to the way in which the Greenwich meridian has been (arbitrarily) selected as the zero point for the measurement of longitude. The zero point chosen on the celestial sphere is the first point of Aries, γ, and the angle between it and the intersection of the meridian through a celestial object and the celestial equator is called the right ascension (RA) of the object. Right ascension is sometimes denoted by the Greek letter α and is measured from 0h to 24h along the celestial equator eastwards (in the direction of a right-handed screw motion about the direction to the north celestial pole) from the first point of Aries, that is, in the opposite direction to that in which hour angle is measured. Like the definition of hour angle, this convention holds for observers in both northern and southern hemispheres. In above figure, the right ascension of the star X is given by the angle -NCP-Y. ( http://abyss.uoregon.edu/~js/ast122/lectures/lec02.html )