Shadow Lengths, September to December
On September 15, students pushed a 30 cm wooden stick straight into level ground in an open part of the schoolyard and marked the tip of its shadow every two hours. On a cloudless day they recorded: 8:00 a.m., 62 cm; 10:00 a.m., 34 cm; 12:00 p.m., 22 cm; 2:00 p.m., 30 cm; 4:00 p.m., 55 cm. They also sketched which direction each shadow pointed. On December 15 they repeated only the noon measurement and got 48 cm from the same stick in the same hole. One student argues that the shadow changes because the Sun travels in a circle around Earth each day. Another says Earth is turning and the Sun only appears to move. The class has one afternoon to collect new data for a science-night display.
1. Describe the pattern in the September 15 data, explain what causes it, and state which direction the shadow pointed at 8:00 a.m. and at 4:00 p.m. Explain your direction reasoning.
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The shadow starts long in the morning (62 cm), shrinks to its shortest at noon (22 cm), then lengthens again by late afternoon (55 cm). The shortest shadow marks the highest Sun in the sky, because a high Sun sends light down steeply and the stick blocks less ground. The direction rule is that a shadow always points away from the Sun. At 8:00 a.m. the Sun is low in the east, so the shadow falls toward the west. At 4:00 p.m. the Sun is in the west, so the shadow falls toward the east. The cause of the whole daily pattern is Earth spinning on its axis; the stick stays put while we turn with Earth, so the Sun appears to sweep east to west and shadows sweep the opposite way.
2. The stick did not change, yet the noon shadow was 48 cm in December instead of 22 cm. Explain what causes this and describe one measurement that would test your explanation.
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Since the stick is identical, the difference must be the Sun's height at noon. In December the noon Sun sat lower in the sky, so light struck the stick at a shallower angle and the shadow stretched farther. That happens because Earth is tilted on its axis and travels around the Sun during the year; in December our part of Earth leans away from the Sun, so sunlight arrives at a lower angle and days are shorter. A good test is to record the noon shadow on several dates spread across the school year and plot shadow length against date. A smooth seasonal curve supports the tilt-and-orbit explanation; a single pair of readings could be a coincidence.
3. With only one afternoon available, what should the class measure to demonstrate the daily pattern, and what precautions should they take so the display is honest?
Read the worked answer
Measure the shadow every 30 to 45 minutes from about noon to 3:30 p.m., recording both length and direction each time. Six or seven points will show the shadow lengthening and swinging toward the east, which is a visible daily pattern, not a single snapshot. Keep the stick, the measuring tape, and the spot the same, measure from the stick's base to the shadow tip, and log the exact time of each reading. If a cloud passes, the shadow edge blurs or disappears, so mark that reading and retake it rather than guessing. The display should also label the date, because a viewer might otherwise assume these lengths hold year-round, when December's noon shadow was more than twice as long.