Studying Shadows

Activity:
Graphing changes in the altitude of the sun over several months.

Science Standards:
Energy & Matter, Patterns of Change

Objectives:

  • The student will measure the changing length of shadows.
  • The student will calculate the altitude of the Sun.
  • The student will graph shadow length and solar altitude vs. time.
  • Materials:

  • gnomens, signs, trees, flag poles, posts (anything that casts a shadow )
  • meter stick
  • scientific calculator
  • graph paper
  • wristwatch



  • Introduction:
    The measurement of time is an important task for any civilized culture. Historically, the task of time measurement was left to astrologers or King's Wise Men. Everyday, they would measure changes in the Sun's altitude (or "perceived height in the sky") as it changes cyclically over the course of the year. At the PSU/GAO, the winter-time noon Sun only reaches 29 in altitude whereas the summer-time noon Sun reaches almost 87 in altitude (the Sun is never directly overhead at the latitude of the PSU/GAO). The small altitude of the Sun results in very long winter-time shadows. The opposite is true for the large altitude for the summer-time Sun. On approximately December 21, the Winter Solstice, the Sun's noon time shadow will be at its longest noon-time length. Conversely, on approximately June 21, the Summer Solstice, the Sun's noontime shadow will be at its shortest length.
    The length of time it takes the Sun to go from its lowest altitude (winter solstice) to its highest altitude (summer solstice) and back down again is defined as ONE YEAR. This cycle from the short noon-time shadow to the long noon-time shadow and back again takes approximately 365.24220 days.

    Directions:
    1. Carefully measure the gnomen's shadow length.  This must be done at exactly the same time every time it is measured. Carefully measure the height of the gnomen; this only needs to be done once.

    2. Determine the Sun's altitude by finding dividing the height by the shadow length and determining the inverse tangent. Record the altitude and the number of days since your first measurement.

    3. Graph the Sun's altitude vs. the number of days since your began the experiment.  Describe the characteristics of the data, what your graph tells you, and any anomalies. What is the rate of change in altitude of the Sun?

    4. Alterations. Using masking tape, place a large "x" on a south facing window such that there is a shadow of the "x" cast on the floor. Using more masking tape, mark the shadow on the floor every hour as it moves easterly across the floor; label the time and date for each mark. The arc that is created will vary everyday, getting larger in the summer and shorter in the winter (shortest arc on Dec. 21). This "masking tape sundial" can be used to keep track of solstices and equinoxes.