A calendar based on the changing shadow of a gnomon (pole) throughout the year and day.

Astronomical Calendar

Introduction
Concepts
Activity 1
Activity 2
Activity 3
Activity 4
Eratosthenes
Last Thoughts

Introduction

I was stumbling around the kitchen making coffee on the morning December 21st,1997, the winter Solstice. It was a beautiful full-bore sunny day. Slowly these two thoughts came together...winter solstice...sunny day. One could easily wait 50 years for a sunny day on December 21st in Eugene, Oregon! Eugene, in the rainy Pacific NW, averages only 1.5 sunny days per December. I jumped on the opportunity.

I quickly scouted out the playgrounds at the elementary schools near my house looking for the best place to make my model. Harris won out having a most excellent steel tether ball pole in asphalt. I was sentimentally partial to Harris anyway because my son went to Harris. That day I marked the end of the pole's shadow with paint as often as I could.

The project then went back on the back burner until March 21st, the Spring Equinox: remarkably another sunny day! I again marked the pole's shadow throughout the day. While doing this I connected the markings making the 2 lines.

 

Please fell free to give me any feedback you have about this project. I'd also appreciate hearing any additional ideas you might have. Sincerely, Jack Van Dusen, 2441 Onyx Street, Eugene, OR 97403-(541)-687-6962 jack_v@efn.org

Concepts

The completed calendar will consists of 4 lines. Three of the lines are the lines traced by the poleıs shadow on the summer solstice (June 21st), the equinox (March 21st or September 21st), and the winter solstice (December 21st).

This photo was taken on the equinox (March 21st). You can see the tip of the pole's shadow at the end of the straight white line.

The 4th line is a line from the pole perpendicular to each of the lines drawn on the solstices and equinox. It marks the apparent noon: the exact midpoint of the day (not 12:00 P.M.). This apparent noon line points directly to the true (not magnetic) North Pole of the earth.

 


Take the class to the model on a sunny day and explain how the model was made. For example: "The winter solstice line (the first day of winter) was made by coming out on December 21st and marking the position of the shadow throughout the day. Later the marks were connected making a smooth curve. On each winter solstice in the future, the pole's shadow will trace out this curved line.

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Activity 1

Demonstrate marking the end of the pole's shadow by marking it with chalk. Say, "For example, if I were marking the pole's shadow today, I would put an "x" here." You are marking the shadow at this point to demonstrate how the shadow lines were made, and so you can observe how much it changes in the next 5 or 10 minutes.

The equinox line (the first day of spring) was made in the same way. The pole's shadow was marked throughout the day, and the marks were then connected. As you can see they made a straight line.

Surprised? I was.

 

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Activity 2

Choose a sunny day. Have students go out to the calendar and mark the pole's shadow throughout the day. Make marks at least every 15 minutes or they will be far apart and hard to connect. I would have 2 or 3 students stay out for half an hour at a time and mark every 5 minutes if possible. You might want to have special marks on the hour. At the end of day take out the entire class and discuss the results.

After 7-10 days repeat this activity and note how much the results have changed. If you used chalk for the first tracing you may have to refresh your first tracing every few days. Poster paint will wash off eventually with water and, if it doesn't rain, may last until your second tracing.

Considerations: The change in the shadow from one day to the next is greatest near the equinox and less near the solstice. So the resulting difference between two tracings will be greater near the equinoxes and less close to the solstices.

Math link: If you labeled the marks made on the hour (8:00, 9:00, etc.) measure the distances between each hour's mark. Then calculate the rate of change for each hour. Calculate as inches per hour and feet per hour. Is the rate constant throughout the day? Predict if the rates would be the same a month later.

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Activity 3

Record from a newspaper the time of sunrise and sunset. Use these figures to calculate the exact midpoint of the day. Check to see if your calculation accurately predicts the time the pole's shadow crosses the apparent noon line.

For example: Today is April 13th and sunrise is 6:33 A.M. and sunset is 7:53 P.M. Since we've already changed the clocks for daylight savings we would expect the apparent noon to be around 1:00 P.M. Let's see.

From 6:33 to 1:00 is 6 hours and 27 minutes. 6 hours and 27 minutes before 7:53 is at 1:26. Splitting the difference between 1:00 and 1:26 is 1:13.

Check: From 6:33 to 1:13 is 6 hours and 30 minutes From 1:13 to 7:53 is 6 hours and 30 minutes. Result: the apparent noon is at 1:13 today.

You can expect your apparent noon to be about this time of day. Will it be this time every day? I DON'T KNOW! I haven't done the experiment yet. Repeat this experiment on several days and let me know.

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Activity 4

A demonstration that shows why the angle of the sun affects how warm it gets.

Materials: a flashlight and some grid paper (1 cm. grid is best)

Darken your classroom and shine the flashlight directly at the grid paper. Count how many squares receive light. If a square is more than half lit count it, less than half, don't count it.

Now shine the flashlight at the grid paper on an angle, but from the same distance. Again count the lit squares. At an angle the light is spread out over more squares. The same amount of light spread out over more squares means less energy for each square.

The main idea is that in the summer the sun's energy is more directly overhead so there is more energy per unit and it gets hotter. In the winter the sun's rays are at more of an angle. The same amount of energy is spread out over more space. So each area gets less energy and doesn't get as warm.

Note: An alternative to using grid paper would be to shine the flashlight at any sheet of paper and trace the outline of the area the light hits. Cut out the tracings for direct light and angled light. You can place the cutouts on the overhead projector and compare them.

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Eratosthenes: The Librarian Who Measured the Earth

Can you accomplish anything practical by observing the sunıs shadow? Well, Eratosthenes accomplished an astounding feat: by observing the sun's shadow, he measured the size of the earth, and proved it was round in the year 200 BC!

Eratosthenes was the head librarian in Alexandria, Egypt. He received a letter from a friend in Syene, which lies on the Tropic of Cancer. His friend passed on the remarkable fact that on the summer solstice the sun would climb to be directly overhead at midday. The sun would shine to the bottoms of the deepest wells, and the buildings would have no shadows.

In Alexandria, the sun was not directly overhead on the summer solstice. It did not shine to the bottoms of wells and a vertical stick had a shadow. How could this be? Eratosthenes figured that if the earth were flat, shadows would be the same everywhere. So the surface must be curved: a sphere.

The next year he went out and measured the midday shadow of a long vertical pole on the summer solstice in Alexandria and it measured 7.2 degrees. There are 360 degrees in a circle. He divided 360 by 7.2 and found that 7.2 degrees was about one-fiftieth of a circle. He then had beatimist, surveyors trained to walk with equal steps, measure the distance between Syene and Alexandria. Multiplying the distance between Syene and Alexandria by 50, his calculated the circumference of the earth to be 24,662 miles. This is only 200 miles off of the actual circumference of the earth All done with only sticks and shadows, careful measuring, and a brilliant human mind...in 200 BC!

And in 1492 AD most people still thought the earth was flat.

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Last thoughts

The earthıs spin, at our latitude (45 degrees N) causes us to race across in front of the sun at 740 miles per hour, At the equator, the spin of the earth creates a velocity of 1046 MPH.


This fact has affected the location of our space platforms. The first rocket Uhuru ("uhuru" being Swahili for "freedom") sent into space by the US was launched from San Marco, off the coast of Kenya. This location was chosen because it was very close to the equator, where the earth's rotation is fastest and it's easier to put objects into orbit. This also allowed for a heavier payload. Also notice the locations of the two space centers in the United States: Houston and Cape Canaveral. Both are about as close to the equator as you can get in the United States.

Some additional resources:
Bill Nye the Science Guy: the Seasons- An excellent half-hour video presentation of how the tilt of the earth causes the seasons.
The Librarian Who Measured the Earth, by Kathryn Lasky. A childrenıs book about Erasthophones that every school library should have.
Resourses about sundials, a related topic
The courtyard at South Eugene High School in Eugene, Oregon has a sundial.
Internet links:
How to set up a sundial: http://www.sundials.co.uk/setup.htm

A human sundial.

 

since May 10th, 2,000

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