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Task 1

Comparing and Scaling Planet Sizes

Scale drawings and models are used to represent objects that are too large or too small to be drawn or built at actual size, such as a planet. While the size of a scale model is different than the actual object, the model and the object should be proportional. Scaling uses a ratio called the scale factor, which compares the measurements of the drawing or model to the measurements of the real object. Consult the Math Review for more help with scale factors.

In this task, you will scale the diameter of each planet in our solar system and start building a model of the solar system.

Estimated time to complete: 1 hour

You will need these materials:

4 pieces of paper or poster board, 8.5” x 11”

scissors

pencil or pen

ruler

compass used to draw circles (optional)

calculator (optional)

Part A

Question

The circle represents Earth. Based on the size of Earth, predict the relative sizes of Earth’s moon, Jupiter, and Mercury by drawing them next to Earth. Remember that Jupiter is the largest planet in our solar system, and Mercury is the smallest. Draw your prediction in the space provided and label your circles.

Lines

Shapes

Fill:

Line:

Width:

Part B

The table contains the planets in our solar system in order of their average distance from the Sun and their corresponding diameters. The first step in creating a model of the solar system is to scale these large diameters into smaller, more manageable numbers. Eventually, we’ll represent these numbers using circles drawn on paper.

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Diameter (km)

4879

12,104

12,756

6792

142,984

120,536

51,118

49,528

Scaled Diameter (cm)

3.5

1.9

The ratio between Earth’s actual diameter and its scaled diameter can be used to find the scaled diameter of the other planets. Earth’s diameter of 12,756 kilometers is scaled to 3.5 centimeters as shown in the table. Now let’s find the scaled diameter of Mars as an example. Using the calculations shown, Mars’s diameter of 6,792 would be scaled to 1.9 centimeters.

d × 12,756 = 6,792 × 3.5

d = 1.9 cm

Use this same process to complete the table with the scaled diameters of the other planets. Round each answer to the tenths place. If you need additional math help, visit the Proportions section of the Math Review.

Part C

Draw each planet on paper using the scaled diameter found in part B. Use a ruler and, if possible, a compass to draw your planets as shown in the images. Notice that in both of these images the radius (half the diameter) is used to create a circle.

If you need help with circles, visit the Properties of Circles section of the Math Review. For assistance with taking measurements, visit Lab Instruments and Measurements.

Be sure to label each planet with its name, and then cut them out. Place the planets in order based on their average distance from the Sun, shown in the table in part B. Now, compare the sizes of the planets. What relationship do you observe between a planet’s size and its proximity to the Sun? If possible, snap a photograph of your model. Click the Insert Image button to add your image file (.jpg or other) in the answer space.

Part D

The Sun has a diameter of approximately 1,391,400 kilometers. How big would the Sun be in your scaled-down model of the solar system? Explain how you scaled the Sun’s diameter to fit into your model, and describe how its size compares to the planets.

Save your paper planets. You’ll use them in the next task.

Task 2

Comparing and Scaling Planet Distances

Now that we have the size of the planets scaled, we need to know how far apart to place them in order to complete our model. In this task, you will scale the distances between the planets and the Sun and complete your model of the solar system. Once again, consult the Math Review as needed for help with scale factors and proportions.

Estimated time to complete: 1 hour

You will need these materials:

toilet paper

pencil or pen

an object and location to represent the Sun

calculator (optional)

large working space, such as a hallway (Make a partial model if your space is smaller.)

Part A

Arrange the cut-out planets you made in Task 1 in order according to their proximity from the Sun, as shown below. As an alternative, you may cut out the scaled planets.

Sun

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

At a large desk or on the floor, choose a position to represent the Sun, and place Mercury a few inches from it. Predict the relative distances between each of the other planets, and space them out accordingly. Do you think the average distances between each of the planets stays relatively consistent or varies greatly? What leads you to this conclusion?

Part B

In a similar way to how you scaled the size of the planets, you’ll also scale the distances between each of the planets and the Sun. The table contains the planets in our solar system and their average distances from the Sun. To more easily compare these distances, you’ll scale them down using sheets of toilet paper.

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Average Distance from the Sun (million km)

57.9

108.2

149.6

227.9

778.6

1433.5

2872.5

4495.1

Scaled Distance (sheets of toilet paper)

5.0

7.6

The ratio between Earth’s distance from the Sun and its scaled distance can be used to find the scaled distance for the other planets. Earth’s distance of 149.6 million kilometers to the Sun is scaled to 5.0 sheets of toilet paper as shown in the table. Now let’s find the scaled distance between Mars and the Sun as an example. Using the calculations shown, Mars’s distance to the Sun of 227.9 million kilometers would be scaled to 7.6 sheets of toilet paper.

d × 149.6 = 227.9 × 5.0

d = 7.6 sheets

Use this same process to complete the table with the scaled distances for the other planets. Round each answer to the tenths place. If you need additional math help, visit the Proportions section of the Math Review.

Part C

Using the data from part B, show the distance from the Sun to each planet by rolling out the correct number of sheets of toilet paper. Place each scaled planet you created in Task 1 at the end of the sheets of toilet paper. For example, Earth would be 5 sheets away from the Sun, while Mercury would be 1.9 sheets away.

Now that you’ve created a scale model of the solar system, describe the relative distances between the planets. What patterns, or similarities, do you notice? How do these distances affect the amount of time it takes each planet to orbit the Sun? If possible, snap a photograph of your model. Click the Insert Image button to add your image file (.jpg or other) in the answer space.

Part D

Astronomers believe that there is a large cloud of frozen comets called the Oort cloud, which surrounds our solar system. It lies approximately 50,000 times farther from the Sun than Earth. Approximately how many squares of toilet paper would you need to put the Oort cloud on your model? Explain how you arrived at your answer.

Part E

Check out how large the Sun appears when the Moon is one pixel wide using this online model of the solar system. Unlike this website, we used one proportion, or scale factor, for the planets’ diameters and another scale factor for the planets’ distances from the Sun. Why do you think it is common to use two different methods of scaling for the planet’s diameters and distances when creating a model?

Part F

Compare your finished model of the solar system to the predictions you originally made about the planets comparative sizes and distances. In what ways were your original predictions about the scale of the solar system correct or incorrect? How has your understanding of the scale of the solar system changed?

Reroll the toilet paper for later use. Recycle the paper planets.

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