Flagpole Shadows: Distance to the Sun or Axial Tilt?
At a school in the northern hemisphere, students measure the length of a flagpole's shadow at local noon on the first school day of each month. The flagpole is 6.0 m tall. Their records are: September 4.2 m, October 5.1 m, November 6.0 m, December 6.5 m, January 6.2 m, February 5.4 m, March 4.0 m, April 3.1 m, May 2.2 m, and June 1.9 m. A student argues that the shadow is shortest in June because Earth is closest to the Sun then, so the Sun must be larger in the sky. Another student says the shadow length is caused by the flagpole getting slightly taller in warm weather. The teacher asks the class to use the pattern, the fixed pole height, and a lamp-and-globe model to evaluate both explanations and to propose what additional data would help distinguish between them.
1. Evaluate the claim that the shadow is shortest in June because Earth is closest to the Sun then.
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The claim does not fit the evidence. The flagpole height is fixed at 6.0 m, so a shorter shadow means the Sun is higher above the horizon at local noon. In the northern hemisphere, the noon Sun is highest near the June solstice because Earth's axis is tilted, not because Earth is closest to the Sun. In fact, Earth is closest to the Sun in early January, when this flagpole's shadow is long (6.2 m). If distance alone controlled shadow length, the pattern would be reversed.
Earth's orbital distance also changes by only about 3%, which is far too small to explain a shadow changing from 6.5 m to 1.9 m. The student has confused a real seasonal pattern with the wrong cause.
2. Explain how a lamp-and-globe model can demonstrate the tilt explanation and what observation would support it.
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Set a globe on a table with its axis tilted about 23.5° and keep the tilt pointing in the same direction as the globe is moved around a lamp. At the position representing June, the northern hemisphere tilts toward the lamp, so light strikes that hemisphere more directly and a small vertical stick's noon shadow is short. At the December position, the northern hemisphere tilts away, light is more oblique, and the shadow is long.
A key control is to repeat the model with the globe's axis vertical. If the shadow length barely changes as the globe orbits, then tilt is necessary to produce the seasonal pattern. The observation supporting the tilt explanation is that the model reproduces the measured short-summer and long-winter shadows only when the axis is tilted and kept pointing the same way.
3. Propose additional data that would distinguish between the distance explanation and the tilt explanation.
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Measure noon shadow lengths at the same latitude in the Southern Hemisphere. If tilt controls the pattern, Southern Hemisphere shadows should be shortest in December and longest in June-the opposite of the northern pattern. If distance controlled the pattern, both hemispheres would have short shadows at the same time of year, because Earth's distance is essentially the same for both.
Another useful measurement is the Sun's noon altitude at two latitudes on the same day. The tilt model predicts systematic latitude differences; the distance model does not. Students could also compare the measured shadow pattern with published Earth–Sun distance data to show that the shortest shadow occurs near the time of greatest distance, not closest approach.