Astronomy with a Stick

AWS Unit 1: Tracking a Moving Shadow

Introduction :: Activity 1 :: Activity 2 :: Activity 3 :: Activity 4

Activity 4

Objective

To show that the Sun reaches its highest altitude a solar noon and then to measure the altitude of the Sun at solar noon over a period of time and record it. The altitude of the Sun is the vertical coordinate of its position. It measures the number of degrees the Sun is above the horizon. In our activities, we will measure the length of the gnomon and the length of the shadow and compute the altitude from that. Measured from latitudes greater than 23 1/2° north or south of the equator, the angle is always less than 90°.

Time Allotment

For one day, the altitude and the azimuth of the Sun can be measured at 10:00  AM, at solar noon, and at 2:00 PM. The class will need to be on the playground briefly for the 10:00 AM and 2:00 PM measurements, and at least 40 minutes for the solar noon measurement. Allow time to repeat these measurements over a series of days, being sure to include the periods of the winter solstice and the spring equinox.

Procedure

Find the altitude of the Sun at 10:00 AM, at solar noon, and at 2:00 PM by measuring the height of the gnomon and the length of the shadow at each time. Have the students record the measurements in their notebooks for later conversion. Also, record the azimuth at each time.

In the classroom, show the students how to lay out the measurements on a piece of construction paper, 12" x 18". A horizontal line, labeled SG, should measure the length of the shadow. A vertical line, perpendicular to SG and labeled GH (use the protractor to measure a right angle), should measure the height of the gnomon. Connect lines SG and GH. This line, the hypotenuse of the right triangle, represents the light rays of the Sun (see figure 5). Find the altitude of the Sun by measuring the angle HSG with a protractor.

This activity should be repeated close to the solstice and equinoxes and at approximately 1- or 2-week intervals. Make a table with the class that includes the azimuths of the Sun, the altitudes of the Sun, and the time and azimuths of sunrise and sunset for each date (the data about sunrise and sunset can be obtained from an almanac, from the newspaper, or from an ephemeris).

Discussion

1. The discussion of these observations of altitude and azimuth should include the following conclusions:
2. The azimuth of the Sun is 180° from north at solar noon each day. This is due south.
3. The altitude of the Sun is highest each day at solar noon.
4. The altitude of the Sun at solar noon changes from day to day. It is lowest in winter and highest in summer. This makes the winter shadows longer than shadows at the same time in summer.
5. The daylight hours vary in relation to the daily changes in altitude and azimuth.
6. The length of daylight hours where we live varies as the Earth revolves in its yearly orbit around the Sun.

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