Society of Amateur Radio Astronomers: Celestial Coordinates

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A Quick Explanation of Celestial Coordinates for the Radio Astronomer
By Jon Wallace

To share information with others, a reference system must be adopted. The system used by astronomers is the celestial coordinate system. After years of teaching that the night sky is not a sphere that rotates around the earth, it is ironic that this is what we are going to envision for our coordinate system. Since both the surface of the earth and the celestial sphere are surfaces of spheres (or nearly so) we can define any point on those surfaces with two coordinates. In nearly the same way that we use Longitude and Latitude to find a point on the surface of the earth, we use Right Ascension (RA) and Declination (DEC) to find objects on the celestial sphere. This is where we should break to make sure that everyone that is about to use this has a radio telescope in which the pointing of the antenna is precisely known. With optical telescopes we can verify our position with a quick glance through the scope but with our radio antenna it's much more complicated. If you need to verify your pointing, here's a way of doing it with no extra cost than the time to complete some days of solar observing.

Verifying Your Pointing Position

I learned from Paul Schuler that you could use the sun as a pretty good point source and plot the width of the solar plot (left and right of center) versus the number of degrees away from the actual/calculated declination. (For this, you must be sure to capture the entire solar peak since you will need the peak to find the centerline). I looked up the sun's actual RA and DEC on Jim Sky's program "Radio Sky Planetarium 1.2" (you could get this many places if you don't own the program) and pointed my antenna directly at the sun and then progressively further away (above and below) to get the plot shown below. I found that my antenna is a little asymmetrical and my pointing is off by about 1.5 degrees (click Here to see chart).

Time (Local Sidereal Time)

Now that you know where you are looking, let's talk about timing and locating objects. If you observer the stars on a daily basis, you may notice that the stars rise and set about 4 minutes earlier each day. This is due to the fact that our earth not only rotates on its axis but revolves around the sun as well. In order for the earth to point directly at the sun on two consecutive days, the earth has to rotate a little more than once (about 1 degree = 4 minutes more). Therefore, a solar day (based on noon to noon) is 24 hours long while a sidereal day (with respect to the stars) is only about 23 hours 56 minutes long.

Sidereal time is the basis of our Celestial Coordinate system since it doesn't vary from day to day. A Solar day can vary. Take for instance the example of placing a stick in the ground and observing the time that the shadow is smallest (when it crosses the north/south meridian line). This time is usually not exactly noon. The shortening and lengthening of the Solar Day is due to the Earth's elliptical orbit so when the Earth is at its closest point to the Sun (perihelion), it moves quickest while at its farthest point from the Sun (aphelion), the Earth moves slowest. This effect accounts for up to 10 minutes difference between the actual Solar Day and the average Solar Day. The Sidereal time is actually the same as Right Ascension discussed below and will be one of our two references on the Celestial Sphere (like latitude and longitude on the earth's surface).

Local sidereal time is used to plan your observation session. Since you can't see what you're aiming for (usually), you must be able to predict when to start your observation session. You will eventually use the Right Ascension and Declination (described below) of an object you want to observe to set up your antenna pointing and start time. Remember the Right Ascension is the same as the sidereal time so knowing your sidereal time allows you to predict when the object will be visible from your site on any day. To find your local sidereal time can be quite a daunting task. If you want to use formulae to calculate it, check out the following site: http://www.btinternet.com/~kburnett/kepler/sidereal.htm>. Otherwise, I recommend either a program or a web site clock. Usually, radio astronomy data collection programs have built in sidereal clocks but if not, I like the program ASTROCLK that you can get free at: http://www.dransom.com/astroclk.html. If you want to use a web based clock, there are a million but try the sidereal time calculator at: <http://tycho.usno.navy.mil/sidereal.html>.

Azimuth and Altitude

If you were to go out tonight and try to show someone the 'Big Dipper' you'd probably point to the object and use Azimuth and Altitude. Azimuth is the angle around the horizontal from due north and running clockwise. It corresponds to the compass directions with 0 degrees representing due North, 90 degrees due East, 180 degrees due South, and 270 due West. Altitude is the height of the object, in degrees above the horizon. Altitude can range from 0 degrees (on the horizon) to 90 degrees (directly overhead). A good approximation of these to use at night is your hand at arm's length. Your whole hand (thumb through pinky) is about 10 degrees and each finger is about 2 degrees. Although Altitude and Azimuth are useful for observing at night and showing others constellations and other objects, it isn't helpful for us. This is because none of us are at the exact same latitude and longitude and so my altitude and azimuth information for the 'Big Dipper' would be different for you. Also, as the object rises and sets, it changes position in the sky.

Graphic used by permission from Dr. Jim McDonald

Notice that the Celestial North Pole has an altitude that is equal to your latitude in degrees.

Right Ascension and Declination

As I mentioned above, Right Ascension (RA) and Declination (DEC) are similar to longitude and latitude. If you picture the earth's North Pole projected into the sky this would correspond to the Celestial North Pole. And if you project the earth's equator into the sky this would correspond to the Celestial Equator. The longitude lines on a celestial sphere are called Right Ascension. Right Ascension is measured on the celestial equator in an easterly direction. Instead of measuring in degrees though, it is measured in hours, minutes, and seconds. A full rotation corresponds to 24 hours, roughly the time it takes for the sphere to rotate once around. Each hour of right ascension is about 15 degrees on the celestial sphere. The Right Ascension of 0 hours occurs on the Vernal Equinox.

Declination is corresponds to latitude and is measured in degrees above or below the celestial equator. An object above the celestial equator has a positive declination; an object below the celestial equator has a negative declination. Since this coordinate system is relative to fixed objects in the celestial sphere, the Right Ascension and Declination don't change and can be shared with anyone on the earth.

Graphic used by permission from Dr. Jim McDonald

Practical Applications/Examples

Optical:

Now that we have a working knowledge of celestial coordinates, let's take a look at how to use them by looking at a portion of an optical sky map and do a few examples. Use the chart that I made (click Here to see chart). to answer the following questions. (You may wish to print out the chart first.)

Fill in the blanks in the following table:

Star #	1	2	3	4	5	6
RA	6:43	7:43	5:53	______	______	______
Dec	-17	+28	+07	______	______	______
Star Name	______	______	______	Castor	Capella	Rigel
Constellation	______	______	______	Gemini	Auriga	Orion

The answers are found at the end of this tutorial.

Radio:

Click Here for a map I made of my observations (plotted as voltages out of 255) with some point sources from charts with their flux in Janskys. When using the chart, remember that lines on the chart represent points of equal flux (intensity). For example: the line marked with a 90 connects all points with values of 90 Janskys. Try the following examples (you may wish to print out the map first):

#1) You find a large peak at 05:33:00 RA, +21:59:00 Dec - What object is it?

#2) You find a small peak at 16:49:00 RA, +15:02:00 Dec - What object is it?

#3) You find a large peak at 12:29:00 RA, +12:31:00 Dec - What object is it?

Answers to Radio Examples are found below:

Conclusion:

I hope you've had no trouble using this and find it of value. If you do have questions, please feel free to contact me through SARA. I'd be happy to try to work with anyone on this or other topics.

Exercise Answers

Optical:

Star #1 = Sirius, Canis Major
Star #2 = Pollux, Gemini
Star #3 = Betelgeuse, Orion
Star #4 = 7:30, +32
Star #5 = 5:14, +46
Star #6 = 5:13, -08

Radio:

#1 Taurus A
#2 Hercules A
#3 Virgo A

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