I. Introduction to the Geographic Grid A. In order to measure accurately the position of any place on the surface of the earth, a grid system has been set up. It pinpoints location by using two coördinates: latitude and longitude. B. It is purely a human invention, but it is tied to two fixed points established by earth motions: the poles, or ends of the earth's rotational axis. 1. Longitude represents east-west location, and it is shown on a map or globe by a series of north-south running lines that all come together at the North Pole and at the South Pole and are the widest apart at the equator -- these lines of longitude are called "meridians." Figure 1 -- meridians of longitude 2. Latitude represents north-south location, and it is shown on a map or globe by a series of east-west running lines that parallel the equator, which marks the midpoint between the two poles all around the earth's circumference -- these lines of latitude are called "parallels." Figure 2 -- parallels of latitude 3. Be aware of the potential for confusing yourself: a. Longitude = E/W location, but it is shown by a series of N/S running lines called meridians. b. Latitude = N/S location, but it is shown by a series of E/W running lines called parallels. 4. If you look at Figure 1 more closely, notice that meridians connect all places on Earth having the same longitude (or E/W location): If you mark a whole bunch of places having the same longitude with dots and then connect the dots, you create N/S running lines, or meridians. 5. Looking at Figure 2 above, notice that parallels connect all places on Earth having the same latitude (or N/S location): If you mark several places having the same latitude with a series of dots and then connect all the dots, you create E/W running lines, or parallels (that are all "parallel" with the equator). C. There is an infinite number of these latitude and longitude lines, because every place on Earth is at the intersection of a particular parallel and a particular meridian. If you had a lot of time and needed to "get a life," you could pinpoint the precise coördinates of every single person reading this lecture or, indeed, of every single person sitting in, say, the campus cafeterias. Each of you right now occupies an earth location, and all locations on Earth can be represented in terms of latitude and longitude coördinates. D. Maps and globes, however, generally only show a few selected (and mathematically convenient) parallels and meridians, e.g., by tens or fifteens or thirties. Otherwise, a map or globe would be one big mess of dark ink! II. Geonerd Bonus: Great and Small Circles A. The geographic grid is built of intersecting great and small circles with with half-great circles. Hunh? 1. Definitions: a. A great circle is created whenever a sphere is divided exactly in half by a plane (imaginary flat surface) passed right through its center. The intersection of the plane with the surface of the sphere is the largest possible circle you could manage to draw on that sphere's surface. Figure 3 -- different ways of creating great circles b. A small circle is any circle produced by planes passing through a sphere anywhere except through its exact center. It will of necessity be smaller than a great circle, hence the clever name. Figure 4 -- a small circle 2. Relevance to latitude and longitude a. The equator is a great circle drawn along a latitude of 0° b. The North Pole and the South Pole are single points at 90° N or S c. All other parallels are small circles drawn parallel to the equator; viewed from above one of the poles, they create a bull's eye pattern in that hemisphere with the pole at the center (see Figure 2. d. All meridians are half-sections of great circles, all of them coming together at both the North Pole and the South Pole (see Figure 1. B. Properties of great circles: 1. They always result when a plane passes through the exact center of a sphere, regardless of the plane's orientation when it enters the sphere. 2. A great circle is the largst possible circle that can be drawn on the surface of a sphere. 3. An infinite number of great circles can be drawn on any sphere. 4. One and only one great circle can be found that will pass through two specified points on the surface of a sphere, unless those two points happen to be exactly opposite one another (antipodes, pronounced "ant-TIP-id-dees"; the singular is antipode, pronounced "ANTIE-pode"). An infinite number of great circles can be drawn through antipodes. For example, the North Pole and the South Pole are antipodal and you can draw an infinite number of meridians (which are sections of great circles) through them. 5. The arc of a great circle is the shortest surface distance between any two points on a sphere: It's the analogy of the old adage about a straight line being the shortest distance between two points (on a plane, that is). 6. Intersecting great circles always cut one another exactly in half. C. Practical uses of great circles: 1. They can be used to find the shortest route for a ship, airplane, or, less happily, a missile that must cross great distances. 2. You can find the great circle route between two places on a globe by stretching a string or rubber-band between any those two locations on the globe: It'll settle on the great circle. 3. When you sample headings for a variety of places on the great circle route and then transfer the resulting line segments onto a flat map, like a wall map, you'll produce a weird-looking path that forms an arc between the two places (instead of a straight line). a. The reason it looks so bizarre is that a globe is a three- dimensional sphere, but a map is a flat two-dimensional representation of that sphere: It is necessarily distorted, so your shortest route looks like a long, circuitous route on the distorted flat map. b. That's why, if you've ever flown from someplace like London to Los Angeles or from, say, Tokyo to New York, they fly you over northern Canada and its Arctic climes! c. You might want to experiment with this with a globe and a flat atlas map to convince yourself of it. Or you can just trust me! D. Enough of great circles and the basic idea of the geographic grid. In the next lecture, I'll expand on the latitude coördinate.
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First placed on web: 09/08/00 Last revised: 09/08/00