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Treebeard's Stumper Answer
12 March 1999

Kidnapped

You're taken in the night and flown to a strange city. When your captors finally remove your blindfold, you find yourself locked in a small room with no windows. There is only a narrow skylight above. You notice that the Little Dipper is higher than normal in Santa Barbara, about halfway between the horizon and straight up. After a while, the stars fade away as sunrise approaches. You can tell it's a big city by the noise. "How odd," you say. "At home in the spring, the sun rises at about 6 a.m., but my watch only says 4:00!" Where are you?

You're kidnapped in the night, but there are clues to your location. The altitude of the North Star in the Little Dipper is equal to your latitude. It's now about 45 degrees, so you've been taken north from Santa Barbara. You notice the sun rises about two hours too early by your watch, which is still on California time. So you're further east by two time zones, about 30 degrees of longitude. Checking an atlas for big cities that match, you're probably in Minneapolis or maybe Chicago. Here in a nutshell, using time and the stars, are the basics of navigation.

Notes:

Clock time within a time zone is everywhere the same, but sun time varies. The sun is not always at it's highest point at noon by the clock since it can only be in one place at a time. At Dunn Middle School, we're within a few miles of the 120 degree longitude meridian at the center of our Pacific Time Zone, so our clock time and sun time are nearly the same. It would be different if we were at the edge of our time zone. (There are other factors such as refraction and the Equation of Time that complicate things.)

If sunrise is exactly 6:00 a.m. and my watch says 4:00 a.m., then there's a two hour difference. I must be 

        degrees    1 day               360
    360 ------- x -------- x 2 hours = --- x 2 = 30 degrees
          day     24 hours              24
to the east of Santa Barbara. If the North Star is exactly 45 degrees high, then that's my latitude (within a degree or so because the North Star wobbles). I must be close to Wausau in central Wisconsin. Celestial navigation is as accurate as the data.

Graybear noticed that:

If your watch doesn't indicate a.m./p.m., you could be at 90 degrees east latitude!
That would put me on the other side of the Earth in Northern China. There are no large cities nearby according to my atlas.

In general, you can find latitude directly by measuring the altitude of the North Star at the end of the handle of the Little Dipper. With a bit of math, you can find your latitude from the Sun or any bright star, at any time. Finding longitude requires an accurate clock and an almanac. This difference shaped history.

It's hard to appreciate the difficulties of navigation in a time with throw-away digital clocks and $99 GPS receivers. A sextant costs much more! But I'm intrigued by the old procedures. There's surprisingly little on the Web about the details of Celestial Navigation. Here are a few useful links to get you started:

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Copyright © 1999 by Marc Kummel / mkummel@rain.org