Do you have a good feel for the size of the Earth? If you’re like most people, you know that it’s big but you don’t have a sense for exactly how big. Today we’re going to change that.
The distance around the equator is around 10 times larger than the distance across the US.
On the Earth, every line of longitude (those are the lines running around the Earth through its North and South Poles) is a great circle, and so is its equator. So let’s use all of this information to think about the size of the Earth in terms of its circumference—which, as we’ve just seen, is the same as the distance around its equator. We discovered earlier that the radius of the Earth is roughly 1.5 times the distance across the US. So how does this distance across the US compare to the distance around the entire planet? Well, geometry tells us that the circumference of a circle is 2π times the circle’s radius. Since π is approximately equal to 3.1, this says that the circumference of a circle is a little more than 6 times longer than its radius.
So in the case of the Earth and our newfound ways of thinking about its size, we’ve just discovered that the distance around the equator is around 1.5 x 6 or roughly 10 times larger than the distance across the US. And if you think about how the US appears on a globe (or better yet take a look at a globe if you have one handy), you’ll realize that this makes perfect sense—the US really does span about 1/10 of the way around the entire planet.
How Big Is the Moon Compared to Earth?
Now that we have an intuitive sense for the size of the Earth, let’s quickly compare that to the size of the Moon. The diameter of our celestial companion is about 1/4 the diameter of the Earth … which is actually a lot bigger than most people think!
This means that the radius of the Moon is also 1/4 the radius of the Earth. Or, thinking about this in our more intuitive way, the radius of the Moon is a little less than half the distance between New York and Los Angeles—which, for those of you familiar with the west coast of the US, is about the distance between Los Angeles and Portland, OR. In terms of circumference, the distance around the Moon is therefore a bit more than twice the distance across the United States.
The Moon is pretty big, but the Earth is definitely a lot bigger. And as we’ve seen, all that you really need to develop a feel for this is a bit of geometrical knowledge and a willingness to take the time to think about things in a way that you can more closely identify with.
Okay, that's all the math we have time for today.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!