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# The Shapes and Size of the Moon

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Author: Janice VanCleave

The different shapes of the Moon as seen from the Earth are caused by different parts of the Moon's surface being illuminated by the Sun. The different Moon shapes are called phases, and all are seen during a period of time called a synodic month.

In this project, you will use the apparent distance to the Moon to experimentally calculate the diameter of the Moon. You will use the known average diameter of the Moon to calculate the percentage of error of your measurements. You will photograph the phases of the Moon and determine the approximate time of moonrise for each phase.

### Getting Started

Purpose: To experimentally calculate the diameter of the Moon.

### Materials

• scissors
• ruler
• index card
• paper hole punch
• yardstick (meterstick)
• transparent tape
• chair
• calculator

Note: This experiment must be performed outdoors on a clear night with a full moon.

### Procedure

1. Cut a 1 × 2-inch (2.54 × 5.08-cm) piece from the index card.
2. Using the paper hole punch, cut a hole in the center of the card. The round hole in the center should have a diameter of 1/4, inch (0.635 cm). The diameter of the hole, 1/4, inch (0.635 cm), will be the apparent diameter of the Moon and will be called D2
3. Lay about 1/2 inch (1.27 cm) of one short end of the card on the zero end of the yardstick (meterstick). Tape the card to the stick and fold the card so that it stands upright, perpendicular to and even with the end of the stick.
4. Outside during a clear night with a full moon, lay the stick over the back of a chair, aiming the end with the card at the Moon.
5. Kneel by the chair with the edge of the stick next to the side of your face (see Figure 5.1).
6. Close one eye, keeping the eye next to the stick open. Look at the Moon through the hole in the card.
7. Move the stick toward, then away from, the Moon until the diameter of the Moon exactly fills the hole in the card. Record the measurement on the stick that is even with your open eye. This is the apparent distance to the Moon and will be called d2. Note that the known average distance to the Moon, called d1, is 235,000 miles (376,000 km).
8. Use the equation below to calculate the diameter of the Moon, which will be called D1.
D1/D2 = d1/d2
9. where

D1 = calculated diameter of the Moon

D2 = apparent diameter of the Moon = width of the hole in the card = 1/4 inch, or 0.25 inch (0.635 cm)

d1 = known average distance to the Moon = 235,000 miles (376,000 km)

d2 = apparent distance to the Moon as measured in step 7

Example:

If d2 is 271/4 inches, or 27.25 inches (69.215 cm), then

D1/D2 = d1/d2

D1 = (d1/d2)D2

= (235,000 miles [376,000 km] ÷ 27.25 inches [69.215 cm] ) × 0.25 inch (0.635 cm)

= 2,155.96 miles (3,449.54 km)

### Results

The experimentally calculated diameter of the Moon using the measurements in the example is 2,155.96 miles (3,449.54 km).

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