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Big and Bigger: How Can the Sizes of Mercury and Earth be Compared?

based on 6 ratings
Author: Janice VanCleave

Problem

How can the sizes of Mercury and Earth be compared?

Materials

  • 12-by-12-inch (30-by-30-cm) piece of white poster board drawing
  • compass
  • metric ruler
  • scissors
  • pen

Procedure

  1. On the poster board, draw a circle with a 3-cm diameter.
  2. Cut out the circle and label it M for Mercury.
  3. Cut another circle with an 8-cm diameter. Label the circle E for Earth.
  4. Lay the circle representing Earth on a table. Determine how many Mercurys will fit across Earth's diameter by laying the Mercury model on the Earth model. Repeat steps 1 and 2 if more than one Mercury model is needed.

Results

The number of Mercurys that fit across Earth's diameter is about 22/3

Why?

The equatorial diameter (the distance through the center of a celestial body at its equator) of Earth is about 8,000 miles (12,800 km). Mercury's equatorial diameter is about 3,000 miles (4,800 km). Thus, Earth's diameter is about 22/3 times bigger than Mercury's diameter. In this experiment, the Earth and Mercury models are made to a scale of 1 cm : 1,000 miles (1,600 km). The diameter of the Earth model is 22/3 bigger than the diameter of the Mercury model.

Big and Bigger

Let's Explore

Compare the equatorial diameters of the other planets in our solar system to that of Earth by repeating the experiment, using the measurements in the Planets' Scaled Diameters table shown here. Note: Large boxes or poster paper can be used instead of poster board to make the larger models. Science Fair Hint: Use photos of the models as part of your display.

Show Time!

  1.  
    1. The diameter of Earth's Moon is about 2,000 miles (3,200 km). Why does the Moon appear to be so small in the sky? Determine how distance affects the apparent size of an object by first measuring the diameter of an object, such as a wall clock. Then stand across the room from the clock. Holding a ruler at arm's length, close one eye and measure the apparent diameter of the clock. Compare the two measurements.
    2. Hold a ruler at arm's length as in the previous experiment to determine the apparent diameter of the full moon. How does this measurement compare to the actual diameter of the Moon?
  2. Big and Bigger

  3. The diameter of the Sun is about 870,000 miles (1,390,000 km). Design a way to make a scale drawing of the Sun using the scale of 1 cm : 1,000 miles (1,600 km). One way would be to draw a circle in chalk on an empty parking lot or outdoor basketball court. Use a strong cord 440 cm long. Lay the cord on the ground. Tie one end of the cord around a piece of chalk. Have a helper hold the free end of the cord against the ground. Keeping the cord taut, use the chalk to draw a circle on the ground as your helper rotates with the end of the cord in the center of the circle. Since about 5 cm of the cord is used to attach the chalk, the circle has an approximate radius of 435 cm. Since a circle's radius is half of its diameter, the diameter of the circle is 870 cm. Display photos of the scale drawing of the Sun.

Check It Out!

The Moon's apparent size is larger when it is near the horizon than when it is high in the sky. This is an optical illusion. What causes this? For information and experiments to explain this illusion, see pages 15–17 in Fred Schaaf's Seeing the Sky (New York: Wiley, 1990).

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