Introduction: As we view the night sky we find that there are objects in the sky: stars, planets, the sun and moon. The location of these objects should be determined so that any change in location can be noted or so that someone else can have the location described to them for their identification. Since the night sky is basically a portion of a sphere, astronomers will use coordinates set up for a spherical system.

This type of coordinate system is not new to us. Positions on the surface of the Earth are given in longitude and latitude. This is a two dimensional system with both sets of coordinates given in degrees. The position of an object on the surface of the Earth can be uniquely determined by its longitude and latitude. If these coordinates are given to another person with a map of the Earth, that person can easily find the location of the object being described.

In a similar fashion, the night sky can be mapped out with a two dimensional coordinate system. There are a couple of different choices here. The first system is referred to as "Horizontal coordinates" and is based on the location of the viewer. The compass directions of North, East, South, and West are part of a full circle surrounding the observer. The circle has 360°, and each of the four compass directions is 90° from the next. North is designated 0° and the degree number increases in a clockwise fashion from North. Hence, East should be at an angle of 90° etc. This compass angle is often called the azimuthal angle or the azimuthal coordinate.

The second coordinate is the altitude of the object. Since stars and other celestial objects are not on the surface of the Earth, we wish to measure how far above the surface they are positioned. Since stellar objects are trillions of miles away and more, we are interested in their angular position above the horizon and not (at this time) their actual distance from the Earth. The altitude is measured from 0° at the horizon to 90° at the point straight overhead, referred to as the zenith. It is not necessary to exceed 90° since a point more than 90° would be behind the observer, and the observer would only need to change their facing (and hence their azimuthal angle) and measure from the new horizon to the point of interest.

Another coordinate system used by astronomers for points on the celestial sphere is called the "Celestial coordinates." Coordinates on this system are not observer dependent. They would be the same for someone in Casper, WY as they would for an observer in Seattle, WA. In this system, an object's position is measured above or below the celestial equator (a projection of the Earth's equator onto the celestial sphere) much like latitude on the Earth. This coordinate is referred to as declination (dec). In addition, an object's position relative to a line passing from the North celestial pole (NCP, a projection of the Earth's north pole) through the vernal equinox (one of two special points on the celestial sphere where the ecliptic crosses the celestial equator) to the South celestial pole (SCP, a projection of the Earth's south pole) is called the Right Ascension (RA). These coordinates will be examined in the exercise below.

Procedure:

Download and install CyberSky if it is not already installed. Start CyberSky From the top line menu, select Options/Location, and set your location to USA, WY, Casper. Click on OK. Make sure that Chart/Horizon Mode is checked.

Click on the "N" button on the toolbar at the top of the screen or press the "N" key on the keyboard so that the screen points toward the northern horizon. From the menu bar, select Chart/Grids. A new window should pop up on the screen. In this window select "Horizontal Grid" and make sure the others are unchecked. Click "OK." This will place the altitude and azimuth grid lines on the screen. Now place the mouse cursor over the "N" on the horizon. Look over to the information bar on the right hand side of the screen and look under the "Horizontal Coordinates." If you don't see the Horizontal Coordinates on the right hand portion, turn them on by selecting View/Pointer Bar or by deselecting View/Data Bar.

Note: It could be the Pointer Bar is present but not all of it is visible. If so, drag it to a convenient location as shown in this movie. Much of this will depend upon your screen's resolution and your window size. For best results, maximize your CyberSky window and set your screen resolution to 800x600 or more. To set the screen resolution in Windows (not CyberSky), select Start/Settings/Control Panel and double click Display. Select the Settings tab and move the slider in the "Screen Area" portion of the window. Click "Apply" or "OK". Note: There are other ways to do this.

Under Horizontal coordinates you will see a set of numbers like 041° 22' 54" +38° 20' 37". Your values depend upon where the pointer is located. If the pointer is not on the sky window, the coordinates space will be blank. The first set of numbers (041° 22' 54" in the example above) is the azimuth. The azimuth coordinates represent the compass directions around the horizon. The second set of numbers (+38° 20' 37" in the example above) is the altitude coordinate. The altitude represents the angular measure of the pointer above the horizon. Note that both coordinates are measured in degrees and parts of a degree. Recall there are 60' in 1° and 60" in 1'.

1) What is the azimuth at the "N" on the horizon?

2) What is the azimuth slightly to the right of North? Slightly to the left?

3) If you start slightly right of North and move towards North, what would you guess the value for North would be?

4) How does this compare with the value you would anticipate if you start from the left of North?

Now click on the "E" button on the toolbar at the top of the screen or press the "E" key on the keyboard. Again place the cursor over the "E" on the horizon. Slightly to the right. The left.

5) What is (are) the coordinate(s) for East? Repeat for the South and West horizons.

6) What is the azimuth for South?

7) What is it for West?

8) What would the azimuth coordinate be for Northeast?

9) Southeast?

Return to a South facing. Place the cursor just above the "S" on the horizon so that the cursor is on the horizon line.

10) What is the altitude of this point?

11) What is the altitude for the grid lines (or curves) "parallel" to the horizon (there should be four such lines)?

12) How does it change if you move along the line to the left or to the right?

13) Near the top of the screen is a circle. What is the altitude for the center of this circle?

14) What is this point called?

From the Chart/Grids menu select Equatorial grid and deselect Horizontal grid. (Equatorial is the same as Celestial.) Notice that the lines are different from what they were before. Notice also that the first set of equatorial (celestial) coordinates is not in degrees. An example of these coordinates might be 13h 22' 37" -48° 55' 17'. The first set of coordinates is the Right Ascension (RA) and is measured in hours and portions of an hour (minutes and seconds). The second set of numbers is declination (DEC) and is measured in degrees and portions of a degree (arcminutes and arcseconds).

Set your orientation to South if it is not already there. Place the cursor just above the "S" on the horizon. Set the time and date to 2/05/2001, 9:00:00 PM.

15) What are the Equatorial coordinates?

16) What are the Horizontal Coordinates?

Now click on the "One Hour Later" button () on the toolbar at the top of the screen. Place the mouse cursor over the "S" on the horizon again.

17) What are the Equatorial coordinates now?

18) What are the Horizontal Coordinates now?

19) What would the Equatorial coordinates be in another hour?

20) What about the Horizontal coordinates?

21) How many hours of right ascension should there be in a full circle?

Return to the northern horizon. Place the mouse cursor on the horizon.

22) What is the altitude coordinate at the horizon?

23) What do you notice about the change in the coordinates above and below the horizon?

Select the "Celestial Equator" from the Chart/Lines menu. Place the cursor over the NCP that is in the middle (or towards the middle) of the screen. Move the cursor up and down.

24) What is the altitude at the NCP (North Celestial Pole)?

25) Look at the location coordinates on the lower right hand corner of the window. Which coordinate (longitude or latitude) is about the same as the altitude at the NCP? Why is it the same?

26) Choose Options/Location and change your location to Mexico City, Mexico. What is the altitude of the NCP?

27) Is that same coordinate about the same as the altitude?

28) Repeat for Anchorage, AK.

29) Repeat for Buenos Aries, Argentina. This will require a little alteration in procedure.

30) What alterations were necessary?

31) Where should 90° in altitude be located?

Return to Casper , WY and the southern horizon. There should be a dark red line going across the screen. This is the "Celestial Equator." Place the mouse cursor over it.

32) What is the declination of the "Celestial Equator"?

Go back to the northern horizon again and place the cursor over the NCP.

33) What is the declination of the NCP?

34) What coordinate system do you think astronomers use most? Why?

35) Why would you use the horizontal coordinates?

36) In what ways, besides astronomy, can you use the horizontal coordinates?

Last revised on 06/13/01