At-Home STEM Activities: Calculate the Diameter of the Moon
Formulate the diameter of the moon using proportions. This activity is geared toward middle- and high schoolers due to the mathematical component.
Background Information:
The diameter of the Moon is proportional to the diameter of a cardboard disk, given that you know the distance to the Moon and the distance to the cardboard disk. The relationship is:
so that:
D = diameter of the Moon
d = diameter of cardboard disk
L = distance to Moon
l = distance to cardboard disk
In this activity, you will measure d and l. You will be given L. You will calculate D.
Materials:
cardboard disk (2 cm* wide works well; you may also use a bigger disk for better accuracy—thus a greater distance, l—or a dime if no cardboard is available to you.
wooden stake (optional)
meter stick* or tape measure
calculator
*Most scientists use the metric system of measurement. Keeping with this practice will benefit your calculations, as metric units are more easily converted.
Process:
Measure the diameter of your cardboard disk (or dime)—that is, the distance from one edge to the other. This diameter, in centimeters, is d.
On a night when you can see the Moon (ideally, it is full or mostly full) place the cardboard disk on top of a stake or on a windowsill, so that the disk exactly covers the Moon from your point of view. If you’re using a dime, hold it at arm’s length.
Ask a helper to measure the distance from your eye to the disk. This distance, in centimeters, is l.
The distance from Earth to the Moon varies between 360,000 and 405,000 kilometers. For this activity, use an average value of 382, 500 km. This distance is L.
Performing your calculations:
Remember that the diameter of the Moon is proportional to the diameter of your cardboard disk in the following way:
so that
Plug your numbers into the above equation and solve for D—the diameter of the Moon.
You do not need to use the same units on both sides of the equation—but d and l must be the same. The solution for D will automatically be in the same units that you used for L. In other words, you may use centimeters for d and l and kilometers for L, to solve for D in kilometers.
Wrapping Up:
Now, look up the known diameter of the Moon:
