## The Horizontal System

The most natural coordinate frame from the observer's point of view is the horizontal frame (Fig. 2.9). Its reference plane is the tangent plane of the Earth passing through the observer; this horizontal plane intersects the celestial sphere along the horizon. The point just above the observer is called the zenith and the antipodal point below the observer is the nadir. (These two points are the poles corresponding to the horizon.) Great circles through the zenith are called verticals. All verticals intersect the horizon perpendicularly.

By observing the motion of a star over the course of a night, an observer finds out that it follows a track like one of those in Fig. 2.9. Stars rise in the east, reach their highest point, or culminate, on the vertical NZS, and set in the west. The vertical NZS is called the meridian. North and south directions are defined as the intersections of the meridian and the horizon.

One of the horizontal coordinates is the altitude or elevation, a, which is measured from the horizon along the vertical passing through the object. The altitude lies in the range [-90°, +90°]; it is positive for objects above the horizon and negative for the objects below the horizon. The zenith distance, or the angle between

Fig. 2.9. (a) The apparent motions of stars during a night as seen from latitude \$ = 45°. (b) The same stars seen from latitude \$ = 10°

the object and the zenith, is obviously

The second coordinate is the azimuth, A; it is the angular distance of the vertical of the object from some fixed direction. Unfortunately, in different contexts, different fixed directions are used; thus it is always advisable to check which definition is employed. The azimuth is usually measured from the north or south, and though clockwise is the preferred direction, counterclockwise measurements are also occasionally made. In this book we have adopted a fairly common astronomical convention, measuring the azimuth clockwise from the south. Its values are usually normalized between 0° and 360°.

In Fig. 2.9a we can see the altitude and azimuth of a star B at some instant. As the star moves along its daily track, both of its coordinates will change. Another difficulty with this coordinate frame is its local character. In Fig. 2.9b we have the same stars, but the observer is now further south. We can see that the coordinates of the same star at the same moment are different for different observers. Since the horizontal coordinates are time and position dependent, they cannot be used, for instance, in star catalogues.

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