When you make an observation or conduct an experiment, you must carefully record data.   In astronomy, one must not only record the values which are measured (the altitude of the sun above the horizon, the position of a planet in relation to the stars, etc.) but also the date and time of the observation (specifying also Pacific Daylight, Pacific Standard, or maybe even Greenwich Mean Time) and the observing conditions at the time (clear, hazy, broken clouds, glow from city lights, etc.).




Many students would like to work in groups while carrying out their Skywatch observations.  We have no objections to this so long as each person contributes to the observations in a significant fashion and each person separately writes up his or her own report.  In such a report, you should mention the names of your collaborators and who did what.




When a scientist communicates results to colleagues, he or she wants to display data in a manner which makes it as easy as possible for the reader to understand.  The data will usually be arranged in a table or in a graph.  It is important that in your Skywatch write-ups you present your data in a clear manner.  Besides a neat "final" display, you must also submit your original notes, sketches, etc., as taken in the field.




In every measurement we make, there is an unavoidable error, regardless of the quality of equipment or observing skill. It is important for a scientist to make a good estimate of these errors.


There are two types of errors: systematic and random.  Systematic errors arise when we consistently perform our measurements in such a manner that they are biased in a particular direction. Such errors can be very difficult to recognize.  The best way to avoid systematic errors is to be very careful in the way the measurements are made.


Random errors are the errors that can never be eliminated, only minimized.  The best way to estimate the size of the random errors is to repeat measurements many times. In general, we get a slightly different value each time the measurement is performed.  The differences between these values provide an estimate of the error.  For instance, if most of a set of measurements of the same quantity fall within a range of 8 units, we might reasonably guess that the random error is about 4 on either side of the average. The average is our best estimate of the measured quantity, but the true value could be as much as 4 higher or lower.


The concept of averaging many measurements of a quantity to obtain a more accurate determination of that quantity is very important.  If the errors in the measurements are truly random, they should nearly cancel each other out in the averaging process.  The more measurements we include in the average, the better the errors will cancel each other.  We should thus repeat measurements as many times as is reasonable and then take the average of all those measurements to arrive at a "best estimate" of the quantity sought.




The question of the number of significant figures in one's measurements is closely related to that of error.  For example, consider a simple homemade quadrant.  With such a device we may be able to measure a star's altitude above the horizon to the nearest half degree.  Thus we might record a measurement of 35.5 degrees.  This measurement has three significant figures.  To quote a measurement of 35.52 degrees made with such a device is misleading because such an instrument simply cannot measure angles to a precision of 0.01 degree.  However, if we were to use a navigator's sextant, we might indeed fairly measure the altitude to be 35.52 degrees.  Because of this instrument's higher precision, we are justified in quoting four significant figures.

When combining measured quantities through arithmetic calculations, the final result should be expressed with no more significant figures than the component with the *least* number of significant figures. For example, suppose we have three quantities of 25.1, 37.22, and 44.33. If we multiply the first two and divide by the third, our answer is 21.1, with three significant figures. We are only fooling ourselves if we read off the calculator and then write down 21.07426122, or even 21.07, since a chain of calculations, no differently than a chain pulling an auto out of a snowbank, is only as good as its weakest link.





SAMPLE SKYWATCH WRITE-UP (for Part A of "Celestial Navigation")


(to give you a general idea)



OBJECTIVES:  To determine the motion of the sun across the sky near noon and thus measure my latitude and longitude.


DATE OF OBSERVATIONS:              October 15, 2001.


WEATHER CONDITIONS:                              fair, with some clouds; little wind.


PROCEDURE:  Outline exactly how you proceeded with your observations, especially if different from the write-ups.


                     Shadow                        Shadow          Sun

Time (PDT)   Azimuth            Length            Altitude (calculated)                                    Comments


11:10               28 deg                   29.8 cm                    34 deg      

11:40               21                        25.3                                    38                                               

11:50               19                        24.9                                    39

12:00               17                        24.5                                    41

12:10 p.m.             ---            ----                                    ----                                                Sun covered by clouds


12:20               12                        23.8                                    42

12:30               10                        23.3                                    43

12:40               9                        22.8                                    43

12:50               7                      22.3                             44                    Stick knocked over by little brother;

                                                                                                            set back as straight as possible

1:00                 4                        21.8                                    44

1:10                 1                        21.7                                    45

1:20                 358                        22.1                                    45

1:30                 355                        22.9                                    44

2:10                 347                        23.7                                    41

2:30                 342                        24.9                                    39                                    Retired from observing



[Here you present the requested plots of altitude angle versus time and the path of the tip of the shadow. You also give your calculations for the longitude and latitude of your observing site, based on your data.]


ERRORS IN MEASUREMENTS:  A brief discussion telling the reader of the estimated errors in your measurements, as well as probable causes. Then estimate how uncertain are your derived values for latitude and longitude.


DISCUSSION OF RESULTS:  Here you tell the reader what you have learned about both the heavens and about how to take observational data, spotlighting any particularly interesting or unexpected results.  You should also mention any new questions your results raise and any suggestions you have for better ways that future Astronomy students might carry out such a Skywatch.