1. Using Math to Understand Our Solar System
Jamie Wolek
Heritage Middle School
Grade 7

2. How many objects in this picture can you name
How many objects in this picture can you name? Do you think the size and “space” between them is accurate?

3. *NOT TO SCALE
Why can’t we find diagrams that are drawn to scale?

4. A scale drawing is one that shows real objects with reduced or enlarged sizes by an amount called the scale factor. To create a scale model of our solar system, we need to reduce the measurements, but keep them proportional.
Neither of these pictures is to scale. The solar system cannot be drawn to scale because if the distances were represented correctly, the individual objects would be too small to see. We are going to create a model that shows distance to scale… we’ll worry about size in the next lesson.

5. 150,000,000 km is about 93 million miles!
What unit of measure is used for measuring distances in the solar system? Meters and kilometers are much too small. Scientists invented the ASTRONOMICAL UNIT to deal with such large distances.
One astronomical unit or AU, is the average distance from the Earth to the Sun (≈ 150,000,000 km).
150,000,000 km is about 93 million miles!

6. You can use unit ratios to convert one unit
of measure to another. For example Jupiter… Jupiter ≈ 778,000,000 km from the Sun How many AU is Jupiter from the Sun? Set up a proportion and solve. 1 𝐴𝑈 150,000,000 𝑘𝑚 = 𝑥 778,000,000 𝑘𝑚 𝒙 ≈ 5.2 AU from the Sun

7. Next, we can use a scale factor to convert AU to centimeters:
𝟏 𝑨𝑼 𝟏𝟎 𝒄𝒎 = 𝟓.𝟐 𝑨𝑼 𝒙 𝒙 = 52 cm
Our scale model of the solar system will have Jupiter 52 cm from the Sun.

8. YOU TRY IT!!!
Mercury ≈ 58,000,000 km
from the Sun
𝟏 𝑨𝑼 𝟏𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒌𝒎 = 𝒙 𝟓𝟖,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒌𝒎 , 𝒙 ≈ 0.39 AU
𝟏 𝑨𝑼 𝟏𝟎 𝒄𝒎 = 𝟎.𝟑𝟗 𝑨𝑼 𝒙 , 𝒙 ≈ 3.9 cm

9. You are ready to represent the distances between different objects in our solar system to scale! Use the following chart to convert kilometers to AU. Then, use a scale factor of 1AU = 10 cm to convert the distance again to use for our model.
Chart will be provided to take notes. It will include planets, moons, and other objects in the solar system.
Distance from
Sun in cm

10. Things to think about… Can you calculate the approximate distance from Earth to the other planets? What would our model look like if we used a different scale factor? Did you notice anything about the distance between planets as they got further from the Sun? Which objects in the solar system have humans reached? Which objects have unmanned spacecraft reached? Which planet seems fit for human exploration and why? Do you think AU are appropriate for measuring distances beyond the solar system?

11. Resources and Image Credits
Solar System Math NASA:
Cover image:
Unlabeled solar system:
Labeled solar system:
Night sky background:
Jupiter
Jupiter
Mercury
Hubble telescope image:
Hubble telescope image: