Earth, Moon, and Sun
What are the Sun’s diameter and distance on the scale of our Styrofoam balls for the Earth and Moon?
Step 1 – Understand the problem
This is basically the same problem we did to figure out the Moon’s distance, but this time we are looking for the Sun’s diameter and distance. There is more than one way to do this, but we’ll do it by finding the Sun’s diameter in terms of Earth diameters, then find the Sun’s distance in terms of Sun diameters.
Step 2 – Solve the problem
We’ll break this into substeps.
Step 2a
The Sun’s actual diameter is about 1,400,000 kilometers. How many “Earth diameters” is this? Show your work.
We simply divide the Sun’s diameter by Earth’s diameter of about 12,800 kilometers.
| 1,400,000 12,800 |
≈ 109 |
Notice how the “kilometers” cancel. So the answer is that the Sun’s diameter is about 109 Earth diameters.
Step 2b
Now, use the fact that the Styrofoam ball representing Earth is about 7.6 centimeters (3 inches) in diameter to calculate the Sun’s diameter on this scale.
The Sun’s diameter on this scale would be about 828 cm.
Note that this answer is easier to understand if we convert it to meters.
| 828 100 |
= 8.28 m |
A distance of 828 centimeters is the same as 8.28 meters; we’ll round this to 8.3 meters.
Step 2c
Let’s next figure out how far the Sun should be placed from Earth in our model. The actual Earth–Sun distance (1 AU) is about 150 million km. How many “Sun diameters” is this?
We simply divide the Earth-Sun distance by the Sun’s diameter of about 1,400,000 kilometers.
| 150,000,000 1,400,000 |
≈ 107 |
The Sun-Earth distance is about 107 “Sun diameters”.
Step 2d
Now calculate the Sun’s distance from Earth on this scale.
From Step 2b, you’ve already found that on the scale of our Styrofoam ball for Earth, the Sun would be 8.3 meters in diameter. We multiply this by the 107 Sun diameters we found in Step 2c.
The Sun’s distance on this scale would be about 888 meters, which we can round to 900 meters.
Step 3 – Explain your result
We’ve found that on a scale where Earth is a 3-inch (7.6 cm) Styrofoam ball, the Sun would be about 8.3 meters in diameter – which would not fit in a classroom because it is much higher than most any classroom ceiling. This model Sun would be located about 900 meters away, which is much farther than most school grounds extend. In other words, it would be very difficult to include a scale model Sun on the same scale we used for the Earth and Moon.