Shadow Sticks and the Sun

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Background:

Our shadows change over the course of the day and through the seasons. When is your shadow the shortest? When is your shadow the longest?

All Photos Courtesy of Dave Kust, Breck School

Materials:

  • Tree or lamp post that is in the Sun most of the day
  • Chalk, stones or rope
  • Pencil or paper
  • Clock
  • Tape measure or yard sticks

Activity:

  1. Select a tree or lamppost that is in the sun most of the day.
  2. Mark off the length of the shadow of the tree several times during the day. Include early in the morning, noon, and late in the afternoon. You can make these marks either by drawing a line with the chalk if there is a sidewalk or parking lot. Or you can lay down small rocks along the length of the shadow.
  3. When is the shadow the shortest? The Sun is highest in the sky at noon and casts the shortest shadow. Does your shadow stick keep as accurate time as a true sundial? Is it as accurate as a watch? What happens if you start at the base of the tree and lay down the rocks? Did the shadow line change too quickly? Did you end up with a crooked line?

About 2000 years ago, scientists discovered that if the shadow stick is slanted, it kept more accurate time than a straight object. The most accurate was if the slanting post (called a "gnomon") was slanted to the same degree as the latitude where it is placed. Then the direction was the same at any hour of the day regardless of the season of the year.

Materials:

  • Long stick or post (gnomon)
  • Protractor
  • Compass
  • Atlas
  • Chalk, stones or rope
  • Pencil or paper
  • Clock
  • Tape measure or yard sticks

Activity:

  1. Using the atlas, look up the latitude of your town. (Minneapolis is about 45 degrees N. latitude)
  2. The post or long stick needs to be inserted into the ground at that angle (45 degrees for Minneapolis).
  3. Using the compass, align the shadow stick so that it points North. The shadow stick or gnomon is now set up in the same direction as the Earth's axis.
  4. Just as you did with the tree or lamppost, mark off the length of the shadow of the shadow stick several times during the day. Include early in the morning, noon, and late in the afternoon. You can make these marks either by drawing a line with the chalk if there is a sidewalk or parking lot. Or you can lay down small rocks along the length of the shadow. The students using rocks may want to mark the top of the shadow first and work their way down to the base of the shadow stick. The shadows can change quickly and if the students start at the base of the shadow stick the shadow lines end up being crooked.

Did the shortest line match when your clock said noon? Probably not! That's because a clock and a sundial are actually measuring two different things. The clock measures the passage of time in minutes. The sundial measures the movement of the earth rotating on its axis. The sundial measures L.A.T. or local apparent time. The LAT differs from season to season and from place to place. The actual day length varies from day to day throughout the year. In addition all sundials do not coincide. That is because the Earth is rotating to the east on its axis at a rate of one degree every 4 minutes. For that reason noon in St. Paul is a few minutes before noon in Minneapolis.

A clock measures L.M.T. or local mean time. LMT measures the average speed at which the Earth rotates 24 hours. Using clocks has been very important in modern times. Time differences between railway stations for instance, became a problem so the standardized method became a necessity.


National Science Education Standards

Earth and Space Science
The sun, moon, stars, clouds, birds, and airplanes all have properties, locations, and movements that can be observed and described. (K-4)

Objects in the sky have patterns of movement. The sun, for example, appears to move across the sky in the same way every day, but its path changes slowly over the seasons.

Most objects in the solar system are in regular and predictable motion. Those motions explain phenomena such as the day, the year, phases of the moon, and eclipses. (5-8)

National Math Standards

Algebra
Analyze change in various contexts.

Measurement
Understand measurable attributes of objects and the units, systems, and processes of measurement.

Apply appropriate techniques, tools, and formulas to determine measurements.

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