How to Use the Stars to Find Your Latitude
Have you ever wondered how people figured out their latitude back in the days before the Internet? Did you know you can use the same math trick they used to pinpoint your latitude today? Keep on reading to find out how it works.
Jason Marshall, PhD
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How to Use the Stars to Find Your Latitude
Greetings, Secret Agent Math! Your mission, should you choose to accept it, is to figure out where you are on Earth relative to the equator. Why might you need to be able to figure this out? Who knows! But a secret agent like yourself is always curious to learn new things, right? After all, you never know when one of these skills is going to come in handy.
Perhaps it’ll be when you’re on that super secret mathematically-oriented spy mission to crack the code used to encrypt that really important message. Or perhaps it’ll be when you’re deploying your particularly well-honed set of mathematical skills to solve that riddle that’s going to help you save those people from that thing. Or … whatever.
The point is, you never know when figuring out where you are on Earth relative to the equator—by which I mean figuring out your latitude—is going to come in handy. So, as every good secret agent skilled in the fine and beautiful art of mathematics has done before, today we’re going to add this trick to our repertoire. Stay tuned to find out how it works!
Recap: What Is Latitude?
Before we rejoin Secret Agent Math and the quest to pinpoint your latitude on Earth, we’d first better recap what we mean by latitude. Those of you who have stared at a globe long enough to notice the grid of horizontal and vertical lines already know pretty much everything you need to understand latitude (as well as its close cousin longitude).
We can mark the location of any point on Earth by specifying its latitude and longitude.
The key thing to know is that we can mark the location of any point on Earth by specifying its latitude and longitude. Lines of constant latitude run around the globe parallel to the equator, while lines of constant longitude run north-south from one pole to the other.
Today we’re going to focus on how you can figure out the latitude of wherever you happen to be standing. In other words, we’re going to figure out how you can find the number of degrees north (or possibly south) of the equator that you are standing. Ready to hone your math secret agent skills and figure it out? Good!
The Boring Way to Find Your Latitude
Like most things you might want to do in life, there’s more than one way to find your latitude. Some ways are easy but boring, and some are a bit harder but much cooler. For the sake of completeness, let’s start with the easiest but also the most un-Secret Agent Math way. Namely, just ask Google.
Yes, that’s right. If you are dying to know your latitude on Earth at this very instant (and who isn’t) and you just can’t bear to wait, you can go to Google and enter something like “latitude of Los Angeles” (or whatever city you’re in). In its nearingly infinite wisdom, Google knows these sorts of things—and it’s happy to tell them to you. Google tells me that my hometown of Los Angeles is located at a latitude of 34.05º N … that’s about 34º north of the equator.
While kind of boring and totally not something a secret agent would use, this trick will nonetheless tell you your latitude wherever you are on Earth. That’s certainly cool, but we can do much better.
The Awesome Way to Find Your Latitude
This brings us to the awesome secret agent approved way to find your latitude. Namely, you can find your latitude using a bit of spherical geometry and the stars! In truth, we’re really only going to need one star: Polaris—aka, the “North Star.” I should say right off the bat that the trick I’m about to describe will only work if you’re in the northern hemisphere (that is, north of the equator). If you’re in the southern hemisphere, you’re out of luck—although there is an analogous trick for the south which you should be able to figure out and put into action once you understand the trick for the north.
You can find your latitude using a bit of spherical geometry and the stars!
Here’s how it works: Imagine standing at Earth’s north pole. Where would Polaris, the “North Star,” be located from your vantage point? If you think about it, you’ll realize that it would have to be directly overhead. And it would always be directly overhead with the entire sky appearing to rotate around it once every 24 hours. Now imagine walking south towards the equator (which actually means any direction). As you walk towards the equator, Polaris will start to move away from the point directly overhead (called your zenith) towards the horizon.
Now, if you were to eventually walk all the way to Earth’s equator, where would Polaris be located? Again, if you spend a few minutes and think about it, you’ll see that the “North Star” would have to be located on your horizon when standing on Earth’s equator. Putting all of this together, we find that all you have to do to figure out your latitude is figure out how far Polaris is above the horizon:
- At Earth’s north pole, Polaris is at your zenith … which is 90º above the horizon. This is also your latitude at the north pole.
- At Earth’s equator, Polaris is on the horizon … so that’s (obviously) 0º above the horizon. Again, 0º is also your latitude if you’re standing at the equator.
- In Los Angeles, Polaris is located about 34º above the horizon. Which, as we’ve already seen, means that Los Angeles is located at a latitude of roughly 34º N.
And that’s all there is to it! The super cool mathematically knowledgeable secret agent method of finding your latitude anywhere in Earth’s northern hemisphere is simply to locate Polaris (which you can easily learn to do) and then estimate the angle between it and the horizon due north of where you’re standing. That angle will always be your mathematically (and astronomically) derived latitude.
Wrap Up
OK, that’s all the math we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.
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!
Map image courtesy of Shutterstock.
About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.