Question

Explain the horizon coordinate system used in astronomy. Show the horizon coordinates of a star on a celestial sphere for an observer at latitude 30°N.

Answer 1

The horizon coordinate system is a celestial coordinate system with the horizon SWNE as the fundamental plane at the observation point. The celestial objects M thus have two coordinates which constantly change: altitude h and azimuth A (which can be measured by convention different ways):

Now imagine we are observing a star M with declination $\delta$ standing at latitude $\phi=30^\circ$ N, and we noticed that its upper culmination was northward from the zenith. Thus its altitude is:

It means that the star has altitude

$$h=90^\circ+\phi-\delta,$$

or in our problem

$$h=90^\circ+30^\circ-\delta=120^\circ-\delta.$$

The azimuth will be the same as for the equatorial coordinate system.