----- The following copyright 1991 by Dirk Terrell
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 Lecture #16    "Where is it?!?!"

   In the interest of clearing away some of the mystery and confusion of 
transformations between the various astronomical coordinate systems, I will 
be posting the definitions of the systems and programs written in QBasic 
that will do the calculations. I hope that you will not view the programs 
as 'black boxes' for doing the calculations, but as sources for learning and 
testing programs that you will write for yourself. These coordinate systems 
are very simple and easy to learn if you go about it the right way. Forget 
spherical trigonometry and memorizing formulae. If you learn to use rotation 
matrices, you will find that you can figure out the formulae in your head.

   The first thing is to figure out whether a coordinates system is right or 
left-handed. In doing this, your thumb represents the positive x-axis, your 
index finger the positive y-axis, and your middle finger the positive 
z-axis. If you draw the x and y axes in the usual way:

                      y
                      |
                      | 
                      |
                      | 
                      --------------x

for a right-handed system, the z-axis comes out of the screen, and a 
left-handed system has the z-axis going into the screen. Point Your thumb in 
the x direction and your index finger in the y direction with each hand and 
you will see how this works. Easy enough.

   Now let's look at a specific coordinate system. Let's define the z-axis 
as pointing toward the zenith (i.e., directly overhead). Let the x-axis 
point toward the north celestial pole. The y-axis will point toward due 
east. Thus the system is left-handed. (Convince yourself of this.) The 
origin of the system (where all the axes meet) is at the observer. The 
system so defined is called the Horizon System (H system). The latitude 
angle of an object referenced to such a system (i.e., the angle between the 
x-y plane (horizon) and a line connecting the object to the origin) is 
called the object's altitude. The longitude angle of the object in this 
system (i.e., the angle gotten by rotating the x-z plane clockwise as seen 
from positive z until the object lies in that plane) is called the azimuth. 
In practical terms, the altitude gives the number of degrees that an object 
is above the horizon. The azimuth tells you how many degrees you have to 
turn from facing due north (turning clockwise from above, that is, when 
facing north, start turning toward east not west) to face the object. An 
object due north thus has an azimuth of 0 degrees. One due south is 180 
degrees, east 90 degrees, and west 270 degrees.

   Next time we'll look at some other systems. The next post is QBasic code 
for computing the altitude and azimuth of an object from its right ascension 
and declination, given local sidereal time and the observer's latitude. 
Don't worry if you don't know what these terms mean. I wrote the program for 
some people who needed this for a telescope, but I figured it would be a 
good thing for us to do in the class. We will learn what all these terms 
mean later.

 Dirk