AST 309--Time
Noon Fix Project

Purpose

In this project, you will observe the Sun and use the observations you make to determine your latitude and longitude on the surface of the Earth. The observation is of a kind that was done by early navigators, and is the simplest form of navigation.

Materials required

To do the project, you will need

1. Your astrolabe

2. Accurate clock or watch, set to the zone time (standard or daylight savings) of your time zone

3. Graph paper

Making the observations

Your observations need to be made both before and after local apparent noon (which will differ from noon as shown on your clock because of your longitude and the equation of time). You therefore need to start observing sufficiently before local noon so that you can get in at least an hours' observations before local noon, and can continue for at least an hour afterwards.

You should record all times in terms of UTC. This means that you have to correct your clock for the difference between Central Standard Time and UTC (+6 hours) or Central Daylight Time and UTC (+5 hours). So, for example, if your clock reads 11:30 and we are on CST, record 17:30; if CDT, record 16:30.

Every five minutes, you should measure the altitude of the Sun, as follows. Hold the astrolabe by the ring so that it hangs freely. Looking at the back of the astrolabe, turn so that the shadow cast by the nut that holds the parts of the astrolabe together falls on the scale around the outside of the astrolabe. When everything is steady, note the angle marked by the center of the shadow. That is the altitude. Record this, together with the time (to the nearest second) in the table. Make these observations every few minutes during the course of the observations.

Reducing the observations

If you did everything right, you will notice that the altitude distance of the Sun slowly increases to a maximum and then decreases again. Plot a graph of the Sun's altitude on the vertical axis versus the time on the horizontal axis. Draw a smooth curve that to your eye best follows the points you have plotted. Because of errors, it may not pass exactly through each point, as shown in the figure below; that's OK. It is more important that the curve be smooth. See the figure at the end of the handout for how it should look.

Next, you need to determine the time that the altitude was a maximum. The best way to do this is to draw a straight horizontal line (it could follow one of the horizontal lines on your graph paper) some distance below the maximum point on the curve so that it intersects the curve you drew in two points, and determine the two times t1 and t2 at which it intersects the curve. The average of those two times is the time of maximum. If draw several different lines at several different times, you will get additional estimates of the time of maximum. The average of several such times is your best estimate of the actual time of local noon.

Finally, draw a vertical line at the time of maximum, and see what the altitude is where the line crosses the smooth curve. That is the altitude of the sun at local noon. Enter 90 degrees minus the Sun's altitude on the worksheet below. That is the Sun's zenith distance.

The declination (celestial "latitude") of the Sun varies during the year, as does the equation of time. Determine the declination of the Sun and the Equation of Time for the day in question using your astrolabe. Write them on the appropriate lines in the worksheet.

Part 0. Essential Information

Date of your observations                     ___________

Correction between Clock time and UTC         +_____hours

Part I. Calculating your Latitude

Zenith Distance (90 degrees - Sun's Altitude) ___________

(plus) Sun's Declination (be careful of sign) ___________

                       (equals) Your Latitude ___________

Part II. Calculating your longitude

          Measured UTC of Local Apparent Noon ___________

                +/- Error of Clock (if known) ___________

          (equals) UTC of Local Apparent Noon ___________

(plus) Correction due to Equation of Time. 
Do not include the correction for longitude!
The sign is as you read it off the scale on
the back of your astrolabe                    ___________

              (equals) UTC of Local Mean Noon ___________

   (minus) Local Mean Time of Local Mean Noon ___12:00__

                      (equals) Your Longitude ___________
     (in hours and minutes West of Greenwich)

  Convert to angle using 1 hour = 15 degrees, 4 minutes = 1 degree.

                            Your longitude is ___________
         (in degrees and minutes of arc West)

Part III. Interpretation

Look up your longitude and latitude on a map or elsewhere. What is the error of your measurement of longitude and latitude?

         Longitude from map ___________ Error ___________

          Latitude from map ___________ Error ___________

Discuss the experiment. What are the major sources of error? Did you obtain accuracy that is consistent with the accuracy of the instruments and method you used? What is the error (in nautical miles) corresponding to the error you actually obtained? (Note that 1 nautical mile = 1 minute of arc, 60 nautical miles = 1 degree.)

For full credit, be sure to turn in all graphs, calculations, and other information that you used in doing this assignment.

Figure 1: Your graph of altitude versus time should resemble this.