DistanceDegrees

Quick Earth Distances

Suppose you need a quick answer to "How many meters is one degree of longitude at 40 degrees North?" and you're out in the field without your Blackberry and GIS software? Do you just let your eyelids droop and your jaw go slack and mutter, "Duh...?"

Well, yes, of course you do. Nobody likes a smartass. But you actually can work this one out without too much math. Just remember a few simple facts:

• The earth is a sphere, or near enough as to make no difference for this parlor trick.
• The old French method for defining the kilometer is that there are 10,000 of them along a line drawn from the equator to the pole, passing through Paris. Since the earth is a sphere, the angular distance from the equator to the pole is 90 degrees and this means that there are 10,000/90 = 111.111 km per degree. This number is also easy to memorize; it's all ones. And if you memorize it in meters, it's just six ones.
• As you go north or south, this distance shrinks by a factor equal to the cosine of the latitude. so at 40 degrees north the distance in meters is cos(40)*111,111m = 85,116m.

If you want to check it, fire up MapInfo and type into the MapBasic Window: Print Distance(-105, 40, -104, 40, "m") and you get 85180. Close enough for rough work. The difference is actually due to the fact that MapInfo uses a distance of 10,007.54 km from equator to pole.