Physics 55 Project:
Measuring the Sun’s Altitude and Direction at Noon
Made available:
Due in class by:
Wednesday, September 7, 2005
Friday, September 23, 2005
Please read through this entire project first so that you have a clear understanding of what is involved before
you start the problem. The total time to obtain and analyze the data should be about an hour.
The following is a simple observational project in which you measure the altitude and direction of the Sun
when the Sun crosses your meridian close to lunch time on some given day (see Figure 2.8 on page 31 of the
text). To complete this project, you will need to have
1. a sunny day,
2. about twenty free minutes centered around 1 pm on that day,
3. a flat open place somewhere on the Duke campus,
4. a tall stick,
5. sunglasses (to see more easily what you are doing),
6. a watch,
7. a compass (which I will loan out to students, please return when done),
8. a string and a simple weight to make a plumb line,
9. a pen,
10. and a clipboard with some paper.
If you have trouble finding any of these items, let me know and I can find something for you from the Physics
demo room.
The project will be easier to do with the help of a classmate (but not classmates, the project is too simple
for three people and a third person will have too little to do), so introduce yourself to someone and make a
new friend if you don’t already know someone in the class. (I can help with the introductions if you are shy.)
As usual, please write down on the front page of your project the name or names of anyone that helped you,
and also as usual make sure that the writing and insights are yours alone; do not copy from a classmates
assignment, even if that classmate was a collaborator!.
If a sunny day and your schedule don’t mesh by the time this assignment is due, you can hand in this problem
separately at the earliest possible next date.
Note: Please, never ever look at the sun directly. This can cause severe and irreversible damage to your
eyes.
Please carry out the following steps:
1. Record the day of your observation (e.g., September 14, 2005) and the place where you carried out
your measurement (e.g., in front of your dorm or in the Duke Garden).
2. Next, obtain a straight stick-like object such as a ruler, yardstick, or broom. The taller the stick, the
more likely you will get better results but don’t choose an object too tall or rounded such as Jame
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Buchanan Duke’s statue in front of the Chapel since you will have trouble determining whether the
object is vertically aligned, what is its height, and the position of the tip of its shadow.
At least ten minutes before 1 pm, insert the stick in the ground so that it is vertical. You can determine
an approximate vertical by a plumb line, which is a weight tied to a string that is hung vertically. (Doing
this part with a friend from class will be helpful here, one person holds the plumb line, the other inserts
and aligns the stick.)
Explain briefly in your homework how you constructed your plumb line and how you aligned the stick
vertically.
3. Now measure and record the height H in meters of the part of the stick above the ground. Two
significant digits is fine here, e.g., 1.5 m.
4. Next, well before 10 minutes to 1 pm, lay down a clipboard with a piece of paper on the ground
such that the tip of the stick’s shadow falls about in the center of the piece of paper. Starting about
10 minutes before 1 pm, start marking the position of the tip of the shadow every three minutes until
about 10 minutes after 1 pm. (Again, this is best done with a classmate, one to hold and read out the
watch, the other to mark with a dot the position of the tip of the shadow.) You should have about six
to eight dots when you are done.
Please be careful not to move the clipboard on the ground while you are recording the position of the
shadow and do not move the clipboard when you are done since you will need to determine the distance
of the tip of the shadow to the base of the stick!
Please hand in this paper (or a xerox of this paper) with the recorded tips of the shadow and also the
times on your watch when the shadow tips were recorded.
5. As best you can, determine and indicate on the paper with some clear marking which shadow tip best
corresponds to the Sun crossing your meridian. Briefly justify your choice.
6. While being careful not to move the clipboard, carefully measure the distance of the shadow tip (that
best corresponds to the meridian crossing) to the base of your stick, i.e., the length L of the shadow
cast by your stick as the Sun crossed the meridian. Record this length in meters in your homework.
7. Next, use your compass to measure the direction of the shadow (from the base of the stick) corresponding to the meridian crossing and write down this direction in your homework. Indicate how accurately
you were able to measure this angle with your compass
You are now done with recording data and can remove the stick and retrieve your clipboard.
8. Use your data to estimate the altitude in degrees of the Sun as it crossed your meridian. You can do
this with a scientific calculator by calculating the following expression:
H
−1
tan
,
L
which is pronounced in English as “the inverse tangent of the ratio of the height H over the length L”.
Note: For this assignment and for the course, you do not need to understand what an “inverse tangent”
means. Just calculate the ratio of H to L on your calculator, then push the “Inverse Tangent” button
on your calculator (on many calculators, you have to push a “Second” button first and then the TAN
key). The observational TA and myself can help you with this if you are not sure what to do. You also
have to be careful to put your calculator in “degree mode” else the above expression will give you an
answer in radians, not degrees.
9. Discuss briefly whether the Sun was directly overhead (at your zenith) when it crossed the meridian.
If not, what is determining the value of its altitude?
10. Explain briefly why the meridian crossing occurs close to 1 pm, not at 12 noon as you might have
expected. (Hint: A full answer can be found somewhere in Chapter S1 of the text.)
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11. For extra credit, try any of the following:
(a) Suggest some ways to improve or to enhance this experiment, e.g., for a future Physics 55 class.
(b) Repeat this experiment a month and two months later and compare your new results with this
homework assignment. Does the direction and altitude change as the weeks pass? If so, can you
explain the pattern of the change?
(c) Make a plot of the tip of the shadow as a function of time and try to find a mathematical expression
to describe the shape that you obtain.
(d) Using your knowledge from Chapter S1, figure out and calculate precisely what is the altitude and
direction of the Sun as it crossed your meridian on the day that you carried out your measurement.
12. What was the total time that it took you to complete this project?
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