**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 at 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 (or close to) the equinox and compare it to their latitude. (See below for a URL which provides dates for future fall and spring equinoxes beyond 1999.)

**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 "one 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.

Look at the __data__ that has been
collected using this activity as a collaborative project.

For examples from schools that have implemented this Activity, see PTK Advocate, Tim McCollum’s Web page:

__http://www.ux1.eiu.edu/~cxtdm/macstu8.html__

Pictures of classes collecting their data:

__Charleston Middle School__

__Muncie Community School__

__Thiells New York__

__Willard Middle School__

__Sacred Hearts Academy__

Tim McCollum's 1999 __Autumnal Equinox Page__.

For more details on procedure, see "The Noon Day Project":

__http://k12.njin.net/noonday/noon.html__

For data gathered on the spring equinox 1998:

__http://geocities.com/Athens/8231/npsbmxpl.html__

The 2000 Vernal Equinox occurs at 2:35 EST on Monday, March 20, when the Sun crosses the equator on its way north for the coming northern hemisphere summer and the southern hemisphere winter. (The southern hemisphere will be observing their Autumnal Equinox.) This 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.

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 the
__tangent table__ or use a
scientific calculator and the following formula to determine the angle between the tip of the
shadow and 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?

**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 summer solstice (the Sun’s furthest position north 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.

Find your __latitude
and longitude__ by entering your city and state.

Look up __Sunrise and Sunset Times__

__US Naval
Observatory Data Services__

Sun and moon rise and set time, Moon phases, eclipses, seasons, postiions of solar system objects,
and other data.

__http://www.windows.ucar.edu/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://aa.usno.navy.mil/data/docs/EarthSeasons.html__

Dates for past and future equinoxes.