From God to Darwin to Black Holes and Back:
The Struggle for Truth in Science and Religion

Spring 2001

Syllabus

Star Day-Sun Day

Class members

Links

Nicenet

Observatory Time

If someone were to ask, "How long is a day?" what would you say? A conventional response to this question might be, "Why, 24 hours, of course." It seems an obvious enough answer. Our clocks reflect this number, whether in the two 12-hour periods of "am" and "pm" or in military time which divides the day into 24 hours. Serious reflection on this problem reveals that the word "day" is actually quite ambiguous as a measurement of time. Before the length of a "day" can be specified, the word must be carefully defined. What exactly is a day? Is a day the time from sunrise to sunset, as opposed to night which is the time from sunset to sunrise? Would measurement of this time period yield the conventional answer of 24 hours? Perhaps a day is the period of time from one sunrise to the next. How would this value compare to our conventional value of 24 hours? Can you suggest other ways of defining the word "day?"

Once the word "day" is explicitly defined as a particular unit of time, it should be possible to actually measure this length of time. One criterion for the validity of scientific measurements is reproducibility. Different people in different locations must be able to perform the same experiment and obtain the same values for a given measurement. Consider the length of a day as the time between consecutive sunrises. Would observers in different places on the earth agree on this measurement? Would this measurement be the same over the course of a year for an observer in a fixed location? By the way, now that we've opened up this can of worms, what is a "year," anyway?

The introduction above was intended to "raise your consciousness" about the importance of assumptions in our daily life. We are quite casual in our everyday usage of language and as long as we agree on our assumptions this normally causes no serious problems in communication. No one in this class has probably ever encountered any difficulty over the ambiguity of how long a day really is. However, now that the question has been raised, what assumptions are involved here? What's the "right" answer? When different answers are possible, the "scientific" solution is to go out and measure for yourself.

In this exercise, you will consider various ways of measuring an interval of time, the "day." We will use as our definition of the word day, that period of time required for either the sun or a star to return to the same spot in the sky. The former is a "solar" or sun day and the latter is a "sidereal" or star day. As you collect data, keep in mind the questions included with this experiment, those formulated in the syllabus and those which arise in lecture during the course.

Reference: Thomas Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Random House, 1959.

1. On at least 10 days, from Feb 6 to Mar 12, observe and record the time when the sun is due south. This will be somewhere around noon. Since accurate time is important for these observations, set your watch to agree with Observatory time, at http://tycho.usno.navy.mil/ Avoid looking directly at the sun for any length of time, so that you do not harm your eyes! Find an appropriate landmark to judge "south" - for example, a north-south sidewalk such as that along the Humanities Building. When the shadow of a light pole points due north, it should be parallel to the sidewalk, and the sun would then be due south. Alternatively, the length of the shadow cast could be measured at several times before and after noon. The time at which the shadow is shortest would then be when the sun was due south. Using the same location each day, record the time, to the nearest minute, when the sun is due south. Describe your viewing location, landmarks and method of measurement.

2. On at least 10 nights, from Feb 6 to Mar 12, observe and record the time when a particular star is due south. Since it is permissible, and even desirable, to look directly at the stars, a slightly different method of determining south is used in this exercise. Practice locating an appropriate star, preferably a fairly bright one, in the southern sky. Rigel in the constellation Orion would be an excellent choice. Sirius is another good choice. Find a building with a fairly smooth east- or west-facing wall which is tall enough to hide your star from view at a convenient time for your measurement. Place one eye close to the wall and sight along it so that you are looking due south. If you are on the east side of the building, locate your star and wait until it moves out of your line of sight behind the building. At the moment when the star just disappears from your line of vision, it is due south. If you are on the west side of a building, you will wait until your star just moves into your line of vision. Using the same location each night, record the time, to the nearest minute, when your particular star is due south. Identify your star and describe your viewing location.

3. Several planets will be visible this month. If you do not know the origin of the word "planet," look it up. Venus is visible in the early evening, while Jupiter, Saturn, and Mars are visible much of the night. Choose two of these planets and record their positions with respect to stars in nearby constellations over the period of time from Feb 6 to Mar 12. Note that the constellations become visible only about an hour after sunset and disappear about an hour before sunrise.

1. Make two graphs, one for the sun and one for Rigel - or your choice of star. Along the horizontal axis, mark the day of the year (37 to 71). Along the vertical axis, mark the time, expressed in minutes after midnight. Begin the vertical axis at the nearest 5 minutes below your earliest time, and end the vertical axis at the nearest 5 minutes above your latest time. Plot your data points, with a small circle around each point. What do you notice about your data? If your observations have been made carefully, you should now be able to draw a straight line through your points. You are permitted - encouraged, even - to generate these two graphs on a computer, including a least squares lines through the data.

2. Determine the slope of the straight line in each graph. Determine (in minutes) the length of the "sun day", and the length of the "star day", based on your measurements and graphs.

The daily observations of each member of the group, signed by the individual, must be included in this report. The actual results of a single individual may be used for the graphs, but each member of the group should report the average values for the length of a star day and a sun day from his or her own data. No more than four people may work as one group.

Report the lengths of a "sun day" and a "star day," in minutes, as determined by your measurements. Are these two values identical? Compare these times with the conventional 1440 minute (24 hour) day. Are they the same? Should any of these three values agree? Justify your answer.

Estimate an experimental uncertainty in the length of your measured "sun day" and your measured "star day". Do either your measured "sun day" or "star day" agree with 1440 minutes within your experimental uncertainty?

Does the word "planet" make sense in relation to your observations? How many planets are there? How many planets can be seen with the naked eye? Which planet was most recently discovered and by whom? Do you think it likely or possible that any more planets will be found?

What was the brightest object you observed in the night sky? The closest? The biggest? What determines the brightness of the objects you observed?

Imagine yourself to be Ptolemy or one of his sympathizers. What assumptions would you bring to these observations? What would you expect to observe? Would any of your data surprise you? How would you account for any discrepancies between theory and data?

Imagine yourself to be Copernicus, Galileo, or one of their sympathizers. What assumptions would you bring to these observations? What would you expect to observe? Would any of your data surprise you? How would you account for any discrepancies between theory and data?

You are simply yourself What assumptions did you bring to these observations? What did you expect to observe? Did any of your data surprise you? A good scientific experiment should not only answer the original question posed, but also raise new questions. Provide one further question this experiment might raise.

Situate yourself in the Universe. Where is your home? Stretch the boundaries of your time and place by discussing Big Bang cosmology and the age of the Universe.

"If the stars should appear one night in a thousand years,
how would we believe and adore,
and preserve for many generations
the remembrance of the City of God?"

Ralph Waldo Emerson

The next several images the views of the sky at 8:30 PM on Tuesday 6 Feb 2001
and at 4:00 AM on Wednesday Feb 7, 2001.