Objectives

Students will measure the length of the shadow cast by a meter stick at midday on the spring and/or fall equinox.

Materials

2 meter sticks

level to ensure the meter stick is vertical

data sheet or log book to record measurements and times

watch

Engage

• Explain the reason for the changing length of the Sun's midday shadow.
• What is the apparent position of the Sun on the equinox?
• At what time would the shadow be shortest? (Hint: solar noon is mid-way between sunrise and sunset which, throughout the year, may not be exactly local noon by the clock)
• Suggest ways in which the angle of this shadow could be measured.
• Predict the angle of the midday shadow on the equinox. Remember, you will be determining the angle of the shadow, not the angle of the Sun above the horizon.

Explain/Explore

The 2002 fall ( autumnal ) equinox occurs at 12:55 a.m. EDT on Monday, September 23rd, when the Sun crosses the equator on its way south for the coming northern hemisphere winter and the southern hemisphere summer. The activity should be conducted as close to that day as possible. If your local skies are too cloudy on Monday, September 23rd, conducting the activity with students on Tuesday, September 24th should still yield fairly good results.

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 each meter stick. A student can then place his/her foot on the bracket resting on the surface, thereby supporting the meter stick in a vertical position. Use a level to ensure that it is exactly vertical. If it's 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 meter stick to measure the length of the shadow. Record the time and shadow length.

Pictures 2001

http://www.ux1.eiu.edu/~cxtdm/equinox_01/equinox_activity_01.html

Pictures from 1999

http://www.ux1.eiu.edu/~cxtdm/Shadows_on_the_Equinox_99.html

Nespelem School 1999

http://www.televar.com/~sedwards/noon.html

Since Washington will still be following daylight savings time, solar noon will occur between 12:30 pm and 1:30 pm PSD. 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

http://aa.usno.navy.mil/data/docs/RS_OneDay.html

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.

Tangent Table

http://passporttoknowledge.com/sun/teachers/tangent.html

Make sure that your shadow length is in centimeters.

Have students use maps or an atlas to find their exact latitude.

• How does the calculated angle of the shadow compare with their latitude?
• What would be the angle of the Sun's midday shadow on the equinox at the equator?

Note: For those wanting to involve all of their 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 noon (by the clock)? Advanced students can research the exact times this occurs at various locations within their time zone. This activity can be repeated up to the winter solstice (the Sun's furthest position south of the equator.)

To report your data, go to the Equinox Shadow Data page. Please forward all data by the end of school on Tuesday, September 24, 2002. To view all submitted school data go to Equinox Project Results beginning Wednesday, September 25, 2002.

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Acknowledgments -

The work from this page (except Nespelem links) is from:

http://ux1.eiu.edu/~cxtdm/equinox_02/noon_shadows_02.html.

Tim McCollum

Charleston Middle School

Special credit to Dr. Michael Leyden of Eastern Illinois University for the original project idea and to Passport to Knowledge (Geoffrey Haines-Stiles Productions) for use of this activity during Live From the Sun (1998-99).

http://www.passporttoknowledge.com/sun/