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Introduction
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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.
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Concepts
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The completed calendar will consists
of 4 lines. Three of the lines are the lines traced by the
polešs 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.
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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.
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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.
Activity
1
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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. |
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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.
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.
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.
Eratosthenes:
The Librarian Who Measured the Earth
Can
you accomplish anything practical by observing the sunšs 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.
Last
thoughts
The
earthšs 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
childrenšs 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:
A human
sundial.
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