Astronomy 1L (Lab Class) Information
Celestial Navigation Project

Motive for Project:
      To force you to learn how to identify stars and constellations which you haven't been shown in class.

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, while you are doing the Altitude-Azimuth Project). You may use any stars that 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 (e.g., from the 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 at least similar (hence, the suggestion that you observe between 6 and 8 stars in each direction).
      If you work with one or two partners, you will have to observe 9 to 12 stars in each direction, in order 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 which are a little to the east of the Meridian, so that you can be aware of when they are exactly due south, or due north. If your observations are a little early, or a little late, not only will you get incorrect results from your calculations, but strictly speaking, you would have to use spherical trigonometry to do the calculations, so you want to make sure that the azimuths of the stars are exactly 180 or 0, and not some in-between value.
      Measure the altitudes of the stars at the time that they are due south or north, and record the time, accurate to the nearest minute, in exactly 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, which 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 detailed 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 might want to estimate the right ascension, using the atlas charts in chapter 7, before hunting through the 300-plus stars in the Appendix, to find the particular ones that 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. In some cases, depending upon how dark your observing location is, you may 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, as 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, do the same thing, 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.

(2) A page containing the two tables which show all your observations and results, as shown above.

(3) A page showing some of (but not all of) your calculations, so that I can see if 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, which shows the place where you made your observations, the calculated "best" latitude and longitude, and an oval whose diameter is twice the standard deviation of your results.