NOON SHADOWS ON THE EQUINOX 2011
Teacher Background
As the Earth progresses in its yearly orbit around the Sun, shadows cast by the Sun vary in length due to the tilt of the Earth's axis (23.5 degrees.) Most students are aware that shadows at midday are longer in the winter and shorter in the summer. What they may not understand is the relationship between latitude and the length of shadows. This is particularly significant on the spring and fall equinox when the Sun's apparent position in the sky is directly above the equator. In this activity students will determine the angle of the shadow cast by the midday Sun on the equinox and compare it to their latitude.
WARN YOUR STUDENTS TO NEVER STARE DIRECTLY AT THE SUN. PERMANENT EYE DAMAGE CAN OCCUR.
Objectives
Students will measure the length of the shadow cast by a meter stick at midday on the fall equinox. They will discover that the angle of the Sun's shadow should be equal to their geographic location in degrees north or south latitude.
Materials
2 meter sticks
level to ensure the meter stick is vertical
data sheet or log book to record measurements and times
watch
scientific calculator or tangent table
Engage
Ask students to explain the reason for the changing length of the Sun's midday shadow. What is the apparent position of the Sun on the equinox? (Above the equator, zero degrees latitude) At what time would the shadow be shortest? (Solar noon. Solar noon is midway between sunrise and sunset which, throughout the year, may not be local noon by the clock) Have students suggest ways in which the angle of this shadow could be measured. Students should predict the angle of the midday shadow on the equinox. Remember, they will be determining the angle of the shadow, not the angle of the Sun above the horizon.
Explain/Explore
The 2011 fall (autumnal) equinox occurs at 5:05 AM EDT on Friday, September 23rd when the Sun crosses the equator on its way south for the coming northern hemisphere winter and the southern hemisphere summer.
Design a device to support a meter stick in a vertical position. Inexpensive shelf brackets can be purchased from a local hardware or discount store and fastened to one end of the meter stick. A student can then place his/her foot on the bracket resting on a flat surface, thereby supporting the meter stick in a vertical position. Use a level to ensure that the meter stick is exactly vertical. If it is not too windy, lay a piece of paper on the ground on which the shadow of the meter stick can be displayed. Teams of students should use a second (and possibly third) meter stick to measure the length of the shadow. Record the time and shadow length.
Residents of Illinois will still be following daylight savings time, and solar noon will occur between 12:30 P.M. CDT and 1:30 P.M. CDT. Determine the time of solar noon for your location. Measurements should be taken at 5 minute intervals for one hour starting 30 minutes before local solar noon.
Calculate solar noon for your location
Select the measurement with the shortest shadow length. Either refer to a tangent table or use a scientific calculator and the following formula to determine the angle between the tip of the shadow and the base of the vertical meter stick: length of shadow divided by 100 = (2nd or inverse function) tangent. You can challenge students to come up with the appropriate formula depending on their mathematical capabilities. Make sure that the shadow length is measured in centimeters.
Have students use maps, an atlas, or a GPS to find their exact latitude. How does the calculated angle of the shadow at solar noon compare with their latitude? (They should be the same) What would be the angle of the Sun's midday shadow on the equinox at the equator? (Zero)
Teacher note: For those wanting to involve multiple classes in this project, shadow measurements can be taken at five minute intervals throughout the day. Mount several meter sticks on a classroom wall, one representing the vertical meter stick casting the shadow, and the others measuring horizontally out from its base. Connect various colored pieces of yarn from the top of the vertical meter stick to the shortest shadow measurement for each class period along the horizontal meter sticks. The resulting display will prove to be a colorful eye catcher which will clearly show the results from each class and make a great tool for comparison of data.
Expand/Adapt/Connect
Is the Sun always at its highest point in the sky at local clock noon? (No, depending upon location) Advanced students can research the exact times this occurs at various locations within their time zone.
The Librarian Who Measured the Earth
More than 2,000 years ago, a Greek mathematician named Eratosthenes used shadow angles to calculate the circumference of the Earth. Without the present day tools of orbiting Earth satellites and global positioning systems, his answer fell remarkably close to our current measurement. Encourage your students to research the method by which Eratosthenes made such an accurate determination. Elementary students will find a delightful book about the life of Eratosthenes titled - The Librarian Who Measured the Earth by Kathryn Lasky.
