NOON SHADOWS ON THE EQUINOX

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 their latitude and the length of shadows. This is particularly significant on the spring and fall equinox when the Sun's position in the sky is directly above the equator. In this activity students will determine the angle cast by the midday Sun on the equinox and compare it to their latitude. (See below for a URL which provides dates for future fall and spring equinoxes beyond 2000.)

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 spring and/or fall equinox. They will discover that the angle of the Sun's shadow approximates their geographic location in degrees north or south latitude.

Materials

2 meter sticks

level to ensure the meter stick is vertical

data sheet per team

stopwatch or watch

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? At what time would the shadow be shortest? (Hint: solar noon is mid-way between sunrise and sunset which, throughout the year, will not be exactly 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.

Explain/Explore

The 2000 fall ( autumnal ) equinox occurs at 1:27 PM EDT on Friday, September 22, 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.

Design a device to set a 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.

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

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. (Or you can challenge students to come up with the appropriate formula, depending on their mathematical capabilities.) 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 Sun compare with their latitude? What would be the angle of the Sun's midday shadow on the equinox at the equator?

Teacher 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, 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.)

Suggested URLs

Note to teachers: please be aware that some sites which may appear in a general search using "equinox" may not be appropriate for students. The ones below, however, provide scientific material directly relevant to this Activity.

http://windows.ivv.nasa.gov/the_universe/uts/equinox.html

What occurs on the equinoxes (includes pictures) if you live at 40 degrees N latitude.

http://hea-www.harvard.edu/ECT/the_book/Chap2/Chapter2.html#oots

Information about Earth's orbit; includes simple classroom activities.

http://www.astro.virginia.edu/~eww6n/astro/

Dates for past and future equinoxes.

http://daily.stanford.org/4-9-96/NEWS/NEWBug09.html

Stanford Daily Online News explains the popular misconception of being able to balance an egg on the equinox. With practice, this is something that you can do on any day of the year.

http://www.cs.ucla.edu/~simonw/sunpos

Sun Position Calculator: using latitude and longitude you can find the sunrise/sunset times for your location and plot the Sun's elevation and bearing over the course of the day.