The Stick That Would Not Move
A class placed a 30 cm vertical stick in the schoolyard and marked the tip of its shadow every two hours on a sunny September day. All marks were made on the same flat pavement. At 8:00 a.m., the shadow was 96 cm long and pointed west. At 10:00 a.m., it was 58 cm long and pointed northwest. At noon, it was 32 cm long and pointed nearly north. At 2:00 p.m., it was 61 cm long and pointed northeast. At 4:00 p.m., it was 102 cm long and pointed east. The students noticed that the shadow changed both length and direction. They also noticed that the stick itself did not move. A classmate claimed, 'The Sun is moving around Earth, which is why the shadow moves.'
1. Describe the pattern in shadow length and direction, and explain why the pattern occurs.
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The shadow is longest in the early morning and late afternoon and shortest at noon. Its direction rotates from west to northwest to north to northeast to east. The stick does not move, so the change must come from the Sun's apparent position in the sky. When the Sun is low in the east, the shadow is long and points west. As the Sun rises higher, the shadow shortens. At noon the Sun is highest in the south, so the shadow is shortest and points north. In the afternoon the Sun appears lower in the west, so the shadow points east and lengthens. A shadow always points away from the light source.
2. Predict the shadow at 6:00 p.m. and justify your prediction using the trend in the data.
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The shadow should be longer than 102 cm and should point generally east or northeast. The trend shows that shadows lengthen after 2:00 p.m. as the Sun gets lower in the west. By 6:00 p.m., the Sun would be lower still, unless it is blocked by hills, buildings, or clouds. A lower Sun angle produces a longer shadow. The exact length cannot be calculated from the data alone because it depends on the Sun's height, but the direction should remain roughly opposite the Sun. If the Sun has set, no clear shadow would form.
3. Evaluate the classmate's claim that the Sun is moving around Earth. Use the investigation as evidence.
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The claim mistakes apparent motion for real motion. The stick is fixed, yet the shadow moves in a regular daily pattern and is shortest near noon. That pattern repeats day after day. The cause is Earth rotating on its axis, which makes the Sun appear to move from east to west across the sky. The schoolyard turns with Earth, so the stick's shadow sweeps around. If the Sun were orbiting Earth daily, the explanation would require a different motion, but the shadow evidence fits Earth's rotation. The Sun is not orbiting Earth each day; the observed change is due to our moving viewpoint.