Shadow Tracking
On a sunny day, students place a 1 m stick upright in the schoolyard and mark the tip of its shadow every hour from 9:00 a.m. to 3:00 p.m. The stick stays in the same spot all day, and the weather stays clear. Their records show: at 9:00 the shadow is 90 cm long and points west; at noon it is 45 cm long and points north; at 3:00 it is 85 cm long and points east. A classmate says, "This proves the Sun travels around Earth, because the shadow moves across the ground." Another student thinks the shadow data can be explained without the Sun orbiting Earth. The teacher asks them to use the pattern in the data to decide.
1. Describe the pattern in the shadow data and explain what it shows about the Sun's position in the sky.
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The shadow changes both length and direction. It is long in the morning, shortest at noon, and long again in the afternoon. It points west in the morning, north at noon, and east in the afternoon. A shadow points away from the light source, so the Sun was in the east in the morning, high in the south at noon, and in the west in the afternoon. The shortest shadow at noon means the Sun was highest then. The pattern is consistent with the Sun appearing to move across the sky from east to west during the day.
2. Explain why the shadow pattern does not prove that the Sun orbits Earth, and describe what is actually happening.
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The shadow only shows that the Sun appears to change position in the sky. The same pattern would be seen if Earth turns on its axis while the Sun stays still. As Earth rotates, the schoolyard turns so that the stick points toward the Sun at different angles during the day. That makes the shadow swing from west to north to east and become shortest when the Sun is highest. To decide between the two explanations, you need more evidence than one day of shadows, such as observations of other objects in the sky. The data alone do not prove the Sun orbits Earth.
3. Predict the shadow's direction and length at about 6:00 p.m., and justify your prediction.
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The shadow should be even longer than at 3:00 and should point toward the east, because the Sun would be low in the west near sunset. The trend in the data supports this: shadows lengthen as the afternoon goes on, from 45 cm at noon to 85 cm at 3:00. As the Sun gets lower, the stick blocks light at a shallower angle, so the shadow stretches farther. The direction continues to swing east as the Sun moves west. The exact length would depend on the Sun's height, but it should be longer than 85 cm.