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# The Shapes and Size of the Moon (page 2)

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Author: Janice VanCleave

### Why?

The equation used in this experiment is called a proportion, a statement of equality between two ratios. A ratio is a comparison of one value to another. Ratios are written as fractions. In this experiment, you used ratios to calculate the diameter of the Moon. These ratios and their proportions are written as D1/D2 = d1/d2, which means the ratio of the calculated diameter of the Moon, D1 to the apparent diameter of the Moon, D2, is equal to the ratio of the known average distance to the Moon, d1, to the apparent distance to the Moon, d2. From this proportion, the diameter of the Moon, D1, is calculated to be 2,155.96 miles (3,449.54 km).

### Try New Approaches

Does the position of the Moon above the horizon affect the results? Repeat the experiment twice, first measuring early in the evening when the Moon is nearer the horizon (a line where the sky appears to meet the Earth). Measure again later the same evening when the Moon is farther above the horizon or near its zenith (a celestial body's point of highest altitude in the sky). Science Fair Hint: Ask a helper to take a photograph of you measuring the apparent distance to the Moon. Use this and your calculations to represent the results of the experiment.

1. Calculate the percentage of error of your measurements using the following example and the known average diameter of the Moon, 2,172.5 miles (3,476 km):
2.

### Example:

• Determine the absolute difference (a positive difference calculated by subtracting a smaller number from a larger number) between the known average diameter and your experimentally calculated diameter:
absolute difference = 2,172.5 miles (3,476 km) – 2,155.96 miles (3,449.54 km)
= 16.54 miles (26.46 km)
• Divide the absolute difference by the known average diameter of the Moon:
16.54 miles (26.46 km) ÷ 2,172.5 miles (3,476 km) = 0.00761(0.00761)
• Find the percentage by multiplying the dividend by 100:
0.00761 x 100 = 0.76%
3. The different shapes of the Moon as seen from the Earth are called phases. These shapes are different amounts of illuminated moon surface and are caused by the Moon's revolving around the Earth. Take photographs or make diagrams of the Moon each night for one synodic month (the time between two successive new moons), 291/2 days. Prepare a display with the photos or diagrams, labeling these phases: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent. For information about the Moon's phases, see Dinah Moché, Astronomy (New York: Wiley, 1996), pp. 196–197.
4. The Moon and the Sun both rise and set in the general direction of from east to west. In the new moon phase, the Moon rises with the Sun and travels close to it across the sky. The Moon rises about 50 minutes later each day in relation to the Sun. Table 5.1 shows the approximate time of moonrise for four moon phases during a synodic month. Use the table to prepare a diagram similar to Figure 5.2.

### Get the Facts

The Earth and the Moon both make shadows. An eclipse occurs when one celestial body passes into the shadow of another celestial body. What are lunar and solar eclipses? During which phase of the Moon do these eclipses occur? For information about the Moon's phases and eclipses, see "Moon" in the World Book Encyclopedia.

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