Let's start off August with a campfire riddle.
Here it is: With the economy so tight we have to send our orders to Santa Claus early. In fact, now that August has arrived, he's already started budgeting for his fuel expenses. Santa needs to know how far it is from the North Pole to Saipan. We have to tell him.
But there's a catch: Santa used to be a Boy Scout. He wants us to go old school. So we have to estimate the distance without using any tools or references; no maps, pens, paper, or calculators.
How do we do this?
Well, if you caught my July 13 column, you may remember this tip for star-gazing: “Make a fist like you’re holding and aiming a pistol, extending your arm out, just like a target shooter. Your fist, at arm’s length, is now covering 10 degrees of vertical arc.”
Let's use this trick to solve our Santa puzzle.
The only real work we have to do is to look due north at night. When we do that, we will see a fairly bright star called Polaris, otherwise known as the North Star. We find it by either knowing our way around the sky, or by observing the sky for long enough to recognize that as the hours go by, all other stars appear to revolve a fixed point in the sky. This point is where Polaris stands. No matter when we look, no matter what time it is, no matter what date it is, no matter what we had for dinner, Polaris is the only thing in the heavens that never moves.
Actually, it does move a little, but not enough to notice for naked-eye estimations.
This isn't a trick we can do in the southern hemisphere, by the way. There is a North Star. But there is not a South Star.
Anyway, now that we've found Polaris, we'll measure its height over the horizon. We extend a fist, which, remember, covers 10 degrees of arc. We will see that Polaris stands one-and-a-half fists over the horizon from Saipan. In other words, it's 15 degrees high.
This leads to a trick used by outdoorsy types, military folks, and other rugged adventurers: The height of Polaris is the same as the observer's latitude. Since it's 15 degrees high, we are at 15 degrees north latitude. Which is to say, we're 15 degrees north of the equator. Same thing, different wording.
Now it's time for the magic number: One degree of arc over the Earth's surface is equal to 60 nautical miles. I think this is the first thing that navigators learn, before they're given a compass or even told where the bathroom is. I've taken the blah-blah-blah out of the magic number, you're just getting the gist for our context.
Now that we know the magic number, we're on a roll. All we need is some mental math.
Since we're 15 degrees north of the equator, we can convert this into nautical miles. We take 15, multiply it by the magic number of 60, and we come up 900. So Saipan is 900 miles north of the equator; I'm just going to say “miles,” not “nautical miles” from now on, with the “nautical” bit being implicit.
Next, I'll consider that the equator is, of course, 90 degrees from the North Pole. So, again applying the magic number, I'll see that the equator is 5,400 miles from the pole. Well, Saipan is 900 miles closer to the Pole than the equator is, so that's 5,400 miles minus 900 miles, which gives us 4,500 miles. That's our answer.
Alternatively, we can just realize that Saipan is 75 degrees away from the North Pole (90 degrees less our latitude of 15 degrees), so we can get our answer in one step by multiplying 75 times 60. I have a hard time doing that in my head, though, which is why I chop things into more manageable chunks. Anyway, 75 times 60 is 4,500. See? Same answer.
So Saipan is 4,500 nautical miles from the North Pole. Indeed, using nothing but eyeball, fist, and brain, you can, from any point in the northern hemisphere, determine your latitude, your distance from the equator, your distance from the North Pole, and the direction of true north (that's why Polaris is called the “north” star). That's a lot of stuff.
For reasons I don't understand, land-lubbers use “statute” miles, not nautical miles. A nautical mile is a little bit longer than a statute mile, with 1 nautical mile equaling 1.15 statute miles. I'll skip metric flavors here, I lack the space.
Santa is an old hand at navigating, so if you tell him “mile,” he'll be thinking nautical, not statute. Now that he's put us in the budget, I've already got high hopes for Christmas.
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Visit Ed Stephens Jr. at EdStephensJr.com. His column runs every Friday.