Shadow Lengths and the Seasons
Each month, students measure the shadow of a 1-m meterstick at 12:00 p.m. clock time on the school playground. Measurements: September 55 cm, October 78 cm, November 103 cm, December 126 cm, January 122 cm, February 95 cm, March 70 cm, April 48 cm. In November the class notes that daylight saving time has ended; in February a fire drill delays measurement until 12:35 p.m. The students conclude that summer is warmer because Earth is closer to the Sun then, and they point to the shorter April shadow as evidence that the Sun is closer. A visitor asks them to separate the effect of the Sun's angle from the effect of Earth-Sun distance and to check whether their measurement schedule is consistent.
1. Describe the pattern in the shadow data and explain what causes it.
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The shadows are longest in December and January, around 122 to 126 cm, and shortest in April at 48 cm. September and March are intermediate, near 55 to 70 cm. At solar noon, shadow length depends on the Sun's altitude above the horizon: a lower Sun casts a longer shadow, while a higher Sun casts a shorter shadow. The pattern is caused mainly by Earth's axial tilt as Earth orbits the Sun. During Northern Hemisphere winter, the North Pole is tilted away from the Sun, so the Sun is lower at noon and days are shorter. During spring and summer, the Sun is higher at noon. The data are consistent with changing Sun angle, not with the students' claim that the Sun itself is physically closer in April.
2. A student claims that summer occurs when Earth is closest to the Sun and that the short April shadow proves the Sun is closer. Evaluate this claim using the data and astronomy.
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The claim confuses distance with angle. Earth's orbit is slightly elliptical, but Earth is actually closest to the Sun in early January, which is winter in the Northern Hemisphere. If distance alone controlled seasons, both hemispheres would have summer at the same time, which they do not. The short April shadow shows that the noon Sun is higher in April than in December, not that Earth is closer. The tilt of Earth's axis changes the Sun's altitude and the length of daylight through the year. The data support the angle explanation: shadows shorten from December to April as the noon Sun rises higher. The class should revise the claim to say that seasonal warmth is mainly caused by more direct sunlight and longer days, not by a large change in Earth-Sun distance.
3. Why could measuring at 12:00 p.m. clock time create a problem when comparing months? How should the class improve the procedure?
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Clock noon is not the same as solar noon. Solar noon, when the Sun is highest, depends on longitude, time zone, and daylight saving time. The November note about daylight saving time means the clock shifted by an hour, so a 12:00 measurement before and after the change is not at the same solar position. The February reading at 12:35 p.m. is also later than the others and would produce a different shadow length for reasons unrelated to season. To improve the procedure, students should find solar noon for their location or measure when the shadow is shortest, record the exact time and date, and keep the method identical each month. They should also note daylight saving changes and avoid taking a delayed measurement as if it were comparable.