SKYWATCH PROJECT: LENGTH OF SIDEREAL DAY
EQUIPMENT REQUIRED: One good eye, a tall building, and a watch (must have a "seconds" hand or digital display).
TIME REQUIRED: A few minutes on each of several nights over at least a week or two.
BACKGROUND: One might think that the sun and the stars move across the sky at the same speed since their motions result primarily from the same cause - the rotation of the earth. The sun's apparent motion, however, is also affected by the orbit of the earth. Because we travel around the sun, we must complete a little more than one rotation for the sun to appear in the same place on two successive days, an interval called a solar day. On the other hand, the earth is so far from the stars that our orbital motion compared to the stars is negligible and a given star will appear in the same place for every rotation of the earth. The time required for this rotation is called a sidereal (star) day. With your naked eye and some care it turns out you can make an amazingly accurate measurement of the length of the sidereal day.
WHAT TO DO: To find the difference between a solar day and a sidereal day you will measure the intervals between the times when a star returns to a given spot over successive evenings. This requires knowing both the position of the star and the solar time when it is at that position. The latter is easy -- you can read it off your watch, although you should carefully check your watch before each observation. Accurate time is available as follows: (1) at 361-8643, (2) from KIRO’s hourly “bong” just as the CBS news begins, or (4) for the cost of a one-minute long distance call to the US Naval Observatory at 202-653-1800.To find the position of the star, note that you don't really need to know the coordinates of the position, you need only to pick a "spot" which can be reliably repeated each night as the star returns. A good way to do this is to time when a star passes behind (is occulted by) a tall building or other object. The edge of the building defines the spot. This would be fine if you could remain at the same location for several nights. But if you must leave during the 24 hours (!), and if you then happened to return to a slightly different location, the edge would be in front of a different place in the sky, resulting in a poor measurement. To minimize this problem move as far away from the building as possible. For example, if you think you can from night to night reproduce your observing location (position of your eye) to within 1 meter the building should be at least 100 meters distant; for 1/2 meter, at least 50 meters distant, etc. A good way to mark your position and sight-line would be with a stick, but this is not necessary if you are careful.
Pick a bright star low enough in the sky that it will soon be occulted by your chosen building from your vantage point. It's simplest if your star is roughly in the southerly direction; if it is not, you will have to think carefully about the star's path across the sky. The best thing to do is to monitor the motions of a few candidate stars over an hour or so, and thus better pick a suitable star, building, and observing location. Having chosen these, record the instant at which the star is occulted by the building. (If you want to improve accuracy, you can repeat this for a second star, which wouldn't have to be using the same building or even the same observing location.) On the next clear evening, return to exactly the same observing location, find your star, and again record the time of occultation. Repeat this on at least 3 nights over a week or two, but 4 to 6 nights over a longer interval yields even better accuracy.
ANALYSIS: Calculate your values for the length of the sidereal day for each of the night-to-night intervals for which you observed. Compare your average measured value and an estimate of its error with the accepted value. How well do they agree? Why do your longest intervals seem to yield the best results? If possible, use a star chart to identify exactly which star(s) you used. Also make a sketch showing your "set-up".