Astronomy 1L (Lab Class) Information
Celestial Navigation Project
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Motives for Project:
      (1) To force you to learn how to identify stars and constellations which you haven't been shown in class, and (2) for those interested in celestial navigation, to learn the simplest method of determining your position from observations of the stars.

Summary of Project:
      Make at least a dozen observations of stellar transits, and use them to calculate your latitude and longitude. A stellar transit is the passage of a star across the Meridian, at the highest point in its diurnal path, directly north or south of the zenith. It does not make any difference when you make the observations. You may make them over a period of weeks, or all on a single night (usually, students do them at the same time as the Altitude-Azimuth Project, for the sake of convenience). You may use any stars you want, but they should cover a wide range of declinations, so that half of them pass to the north of the zenith, and half pass to the south. You will have to learn how to use the text to identify the stars that you observe.
      The analysis of these transit observations is fairly simple. For extra credit, you may also analyze non-transit observations (for instance, from your Altitude-Azimuth Project), using spherical trigonometry.
      If you are working alone, you should observe 6 to 8 stars to the north of the zenith, and 6 to 8 stars to the south of the zenith. The number of stars observed in each direction does not have to be the same, but should be similar. Otherwise, the simplified discussion of determining the accuracy of your observations (as stated below) would not be statistically valid.
      If you work with one or two partners, you have to observe 9 to 12 stars in each direction to receive the same credit as a person working alone would receive for observing 6 to 8 stars in each direction.

Making the Observations
      Watch for stars that are a little to the east of the Meridian, so you can notice when they are exactly due south or due north. If your observations are a little early or a little late, you will get incorrect results from your calculations (though you could use spherical trigonometry to do such calculations, odds are you don't know spherical trigonometry or would just as soon forget you ever learned it), so you want the azimuths of the stars to be exactly 180 or 0, and not some other value.
      Measure and record the altitudes of the stars at the time that they are due south or north, and record that time, accurate to the nearest minute, in the same way as in the altitude-azimuth project. You can refer to the discussion of that project for suggestions on how to do the measurements as accurately as possible. The only difference between the observations for the two star projects is that in the alt-azimuth project you observe the same stars over and over throughout the night, regardless of their location, whereas in the navigation project you only observe stars when they are exactly north or south.

Recording the Results of Your Observations
      You can record the results in any way that you want, but I would suggest an organized list, similar to the one for the alt-azimuth project, that includes spaces for the name of each star, the date and time of your observation, and its altitude and azimuth at that time.

Doing the Calculations Required to Find Your Latitude and Longitude
      Refer to Navigation Calculations for a discussion of the arithmetic involved in finding your position. For each star, you will need to look up its right ascension and declination in Appendix 2 of your text, prior to doing the calculations. Stars are listed in this Appendix in order of their right ascension, so you should estimate the right ascension using the atlas charts in chapter 7, before hunting through the 300-plus stars in the Appendix to find the ones you observed.
     Note For Stars Passing Below Polaris: The current version of the Navigation Calculations page presumes that stars with azimuth zero pass above Polaris. If you are at a relatively dark-sky site, you may be able to see stars passing below Polaris. A future version of the Calculations page will explain things in more detail, but for now, simply adjust the declination and right ascension as follows:
     (Right Ascension) Add or subtract 12 hours from the star's right ascension.
     (Declination) Subtract the star's declination from 90 degrees, then add the result to 90 degrees.

Organizing and Obtaining Your Results
      Construct two tables on a single sheet of paper, in the manner shown here:

Northern Stars (Azimuth = 0)
Star Date/Time Altitude Right Ascension Declination Latitude Longitude
Kochab Some evening xx hh mm + xx N xx.x W xxx.x
             
latitude 1 = (average and standard deviation), longitude 1 = (average and standard deviation)

Southern Stars (Azimuth = 180)
Star Date/Time Altitude Right Ascension Declination Latitude Longitude
Sirius Some evening xx hh mm - xx N xx.x W xxx.x
             
latitude 2 = (average and standard deviation), longitude 2 = (average and standard deviation)

best estimate of latitude = (average of two values +/- larger standard deviation)
best estimate of longitude = (average of two values +/- larger standard deviation)

      For each star, place the observed values in the appropriate boxes, look up the right ascension and declination and place them in their boxes, then perform the calculations required to obtain latitude and longitude. After finding all the northern transit results, take an average and standard deviation, using the techniques shown in part 3a of the Mercury Project, to get latitude 1 and longitude 1, the best estimate of your position from the northern transits. After finding all the southern transit results, use the same procedure to get latitude 2 and longitude 2, the best estimate of your position from the southern transits. After finding these values, take the average of the two latitudes, and of the two longitudes, to get the best estimate of your position from all of your observations.

Organizing Your Report
      Assemble four sheets of paper, and turn them in to me, on or before the night of the Final:
(1) A Cover Page, similar to the one for the Alt-Azimuth Project, detailing everything (as briefly as possible) that I need to know about how you did your project, and how you want credit assigned if you worked with a partner (or two).
(2) A page containing the two tables that show all your observations and results, as shown above.
(3) A page showing some (but not all) of your calculations, so I can see whether any errors in your results are due to blunders in your arithmetic, or to errors in your observations.
(4) A map or tracing of a map that shows the place where you actually made your observations, your calculated "best" latitude and longitude, and an oval whose diameter is twice the standard deviation of your results.