The equatorial system
 

If we extend the plane of the Earth’s equator, it will cut the celestial sphere in a great circle called the celestial equator. This circle intersects the horizon circle in two points W and E (figure 1). It is easy to show that W and E are the west and east points. Points P and Z are the poles of the celestial equator and the horizon respectively. But W lies on both these great circles so that W is 90◦ from the points P and Z. Hence, W is a pole on the great circle ZPN and must, therefore, be 90◦ from all points on it—in particular from N and S. Hence, it is the west point. By a similar argument E is the east point. Any great semicircle through P and Q is called a meridian. The meridian through the celestial object X is the great semicircle PXBQ cutting the celestial equator in B (see figure 1).

Figure 1. The equatorial system.

In particular, the meridian PZT SQ, indicated because of its importance by a heavier line, is the observer’s meridian.
An observer viewing the sky will note that all natural objects rise in the east, climbing in altitude until they transit across the observer’s meridian then decrease in altitude until they set in the west. A star, in fact, will follow a small circle parallel to the celestial equator in the arrow’s direction. Such a circle (UXV in the diagram) is called a parallel of declination and provides us with one of the two coordinates in the equatorial system.
The declination, δ, of the star is the angular distance in degrees of the star from the equator along the meridian through the star. It is measured north and south of the equator from 0^◦ to 90^◦, being taken to be positive when north. The declination of the celestial object is thus analogous to the latitude of a place on the Earth’s surface, and indeed the latitude of any point on the surface of the Earth when a star is in its zenith is equal to the star’s declination. A quantity called the north polar distance of the object (X in figure 1) is often used. It is the arc PX. Obviously,
 

north polar distance = 90^◦ − declination.
 

It is to be noted that the north polar distance can exceed 90^◦.
The star, then, transits at U, sets at V , rises at L and transits again after one rotation of the Earth. The second coordinate recognizes this. The angle ZPX is called the hour angle, H, of the star and is measured from the observer’s meridian westwards (for both north and south hemisphere observers) to the meridian through the star from 0h to 24h or from 0^◦ to 360^◦. Consequently, the hour angle increases by 24h each sidereal day for a star.