Scale Model Earth-Moon Distance
How can you figure out the correct answer for how far the Moon should be in your Earth-Moon scale model?
Step 1 – Understand the problem
You are trying to figure out where to place the Moon in a scale model for which you are using a 3-inch (7.6 cm) ball to represent Earth. The easiest way to do this is to figure out how many Earth’s you would have to line up in a row to make the Earth-Moon distance; that is, how many “Earth diameters” make the Earth-Moon distance? Once you answer that, you can just multiply by the size of your scale model Earth to figure out the Earth-Moon distance on the same scale.
Step 2 – Solve the problem
We’ll start by answering the question of “how many” Earth diameters make the Earth-Moon distance, then use this to figure out the distance with a particular scale model Earth.
Step 2a
What data do you need to answer the “how many” question?
You’ll need to know the two distances: (1) Earth’s diameter and (2) the actual Earth-Moon distance. You could easily look these up for yourself, but we’ll give you the data:
- The Earth–Moon distance is about 384,000 kilometers
- Earth’s diameter is about 12,800 kilometers
Step 2b
What math operation should you use to answer the “how many” question? Your basic operation choices are addition, subtraction, multiplication, or division
The answer to any “how many” question should be a number without any units, and the only operation that will leave you with a unitless answer is division, because the units of kilometers appear in both the numerator and denominator and therefore cancel:
| Earth-Moon distance in “Earth diameters” |
= | Earth-Moon distance Earth’s diameter |
| | = | 384,000 12,800 |
| | = | 30 |
Step 2c – Solve the problem
You now know that the Earth-Moon distance is 30 Earth diameters (that is, 30 times Earth’s diameter), so now you just need to multiply the size of your scale model Earth by 30. The final step in solving the problem is to see what this means for your scale model.
Since your model used a 3-inch (7.6 cm) ball for Earth, the distance to your Moon ball should be 30 times that:
or
30 × 7.6 cm = 220 cm.
Step 3 – Explain your result
The distance in your model should be 90 inches, which is 7 ½ feet, and is also the same as 220 cm, or 2.2 meters. You have already seen this in the activity making the Earth-Moon model.