## Latitude

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Suppose you’re on the open seas, and your GPS falls overboard.  Or maybe it’s 400 years ago.  How can you tell what your latitude and longitude are?

We’ll start with latitude, because it’s easier.  A LOT easier.  If it’s a nice night, and you’re somewhere in the Northern Hemisphere, the easiest way is to take a gander at the North Star using an astrolabe.  Some astrolabes are simple, others are complicated, but they can all be used to find the North Star.

Hey, how about if Godzilla shows us how to use a homemade one!

This model was originally designed by…someone.  I don’t actually know who came up with it.  But all you need is a protractor, a straw, tape, string, a weight, and someone to drill the hole in the protractor so you can attach the string [or you can use a paper protractor].

In theory, the bottom of the straw should be held up to the eye.  Godzilla’s short arms aren’t really conducive to holding things up (he’s had to survive using his brains as much as his brawn), so here’s a drawing of what it would look like:

When you look through the straw at an object like the top of a tree or the North Star (Hmm, why didn’t I draw a star?  Because Godzilla was actually facing tree in our yard at the time, so I got distracted).  Anyway, when you look through the straw, the weight causes the string to fall right at the angle that the object is above the horizontal!

Here’s why:

So sailors just grab their handy dandy astrolabe, measure the distance of the North Star above the horizon, and that’s the latitude!  [I always have to think that one through.  On the equator, the North Star would pretty much be on the horizon, so that’s 0° above the horizon, and at the North Pole the North Star would be directly overhead, which is 90° above the horizon.]

Next up:  Longitude (Part I and Part II).

### 6 Responses to “Latitude”

1. Sue Says:

Nice! I’d like to try this…

2. Ξ Says:

The first student I had who made this (which is actually where I learned about it) went outside, calculated her pace, used that to figure out how far she was standing from our building and then used the angle (plus her height up to her eyes) to calculate the height of the building. If I’m remembering right, it didn’t really match the official height. I think there were too many places where there was potential error. Still, it was fun.

3. Sue Says:

You might be interested in something Tom Davis wrote. His website is http://www.geometer.org/mathcircles/ And if you go down about halfway, you’ll see a pdf labeled Geometry and Geography. He did a great presentation at the Great Circles conference at MSRI.

4. Ξ Says:

Sue, I had a chance to look around that site last night and there are some really great things there! Thanks for pointing it out — I really like all the questions he asked on that article.

5. Dave Richeson Says:

I spent a semester in college sailing. They required us to learn celestial navigation. Many people hated it. I loved it. It was fascinating (and very math-y).

Shooting stars is very, very difficult. Stars are dim and small, sailboats have have an annoying tendency to not stay still, plus to use a sextant you must be able to see the horizon, which you can ordinarily do only at dusk and dawn. Shooting the moon is easier, and shooting the sun is easier still.

You can use the sun to find latitude too—and without a timepiece. You can use a sextant to find the the maximum altitude of the sun during the day. This is easily determined on a sunny day at a time called “local apparent noon”. If you know the declination (the tilt of the earth) it is a simple calculation to find your latitude. Determining the declination requires knowing the date and having an almanac.

Thanks for the fun posts. They bring back great memories!

6. Recommended readings 6/5/09 « Division by Zero Says:

[…] Latitude, longitude, and more longitude ~ I have fond memories of doing celestial navigation […]