Richard Renneboog,GPS


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GPS (Global Positioning System)

Richard M. J. Renneboog
Information Technology Developer / Webmaster
Renaissance Aeronautics Associates Incorporated

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The GPS, or Global Positioning System, is the high-tech application of one of the most fundamental principles of geometry. The word 'geometry' is made up from two Greek words: 'geos' meaning 'earth', and 'metros' meaning 'measure'. Geometry is literally and figuratively 'earth measurement', and everyone has at least heard of the geometric principle of triangulation. There are very rigid rules that apply to the structure of the triangle: the three angles that make up the points of the triangle must add up to 180 degrees, and each of the three sides must be straight lines. Triangulation is the process of describing a point in space as the third point of a triangle irrelative to two other fixed points. Using triangulation, one can determine the exact location of a point simply by knowing one linear distance between two points and two angles, one at each of those points.. Of course, the more exactly one can measure the linear distance and the two angles, the more accurately one can determine the position of the third point, or 'apex'. Here is a very simple example: 'Bob' finds a really tall tree while walking in the forest one day, and is curious about its height. He can't climb the tree to measure it; that simply would not work because his measuring tape is only 25 feet long. But 'Bob' can actually measure the tree without setting foot on a single branch! From the base of the tree, he measures out 75 feet in a straight line. Then, from this point, he measures the angle between the ground and the line of sight from his measured point to the top of the tree. The angle turns out to be 60 degrees. The angle at the base of the tree is 90 degrees, because the tree grows straight up from the ground. 'Bob' can now use the geometric ratios of right-angled triangles to calculate the height of the tree. The tangent of an angle is equal to the length of the side opposite from it divided by the length of the side next to it. In this case, the tangent of the 60 degree angle that 'Bob' measured is equal to the height of the tree divided by the distance to the tree (75 feet). This also means that the height of the tree is 75 feet times the tangent of 60 degrees, or just over 103 feet .

Surveyors routinely use geometry and triangulation to map and lay out areas of land. Until recently they used high quality optical telescopes called 'theodolites' and mechanical measuring devices to carry out the surveying process. But as technology has changed, so has the surveyor's craft. The laser, digital electronics, space travel, and several other technological advances have all combined to make surveying and triangulation far more precise and accurate than they used to be, and allow measurements to be routinely obtained from distances that traditional surveyors could only dream about.

GPS, the Global Positioning System, has come about as a natural development of the advances in surveying technology. It consists of a series of 24 satellites in orbit 11,000 miles (17,600 kilometers) above Earth. Each satellite orbits Earth once every 12 hours, and each carries a highly accurate clock with the ability to measure time to 3 billionths (0.000000003) of a second. All 24 of the satellite clocks are synchronized with each other and each one broadcasts its own time signature. The GPS receiver is programmed to read the time signature of four satellite signals, and to measure the difference in time between receipt of the four signals. Since the signals all travel at exactly the same speed (the speed of light), and all of the satellites are different distances away from any particular point on the planet, each signal takes a measurably different amount of time to reach a particular receiver. This time difference is used by the receiver to calculate the distance to each of the four satellite sources and thus triangulate the exact location of the receiver on the planet's surface. To complete the system, 5 ground stations located throughout the world monitor and maintain the proper functioning of the satellites.

The GPS can fix one's location anywhere on the planet to within a few inches. This allows very precise navigation and control of the movement of people and things on the planet's surface. Unfortunately, this sort of accuracy could be useful to an enemy. The U.S. government intentionally scrambles the signal slightly to reduce the available accuracy, just enough to avoid untoward use of the positioning system while maintaining an acceptable degree of accuracy for the system to be generally useful. The GPS is already being used to produce the most accurate maps ever, for surveying and documentation, for prospecting, for on-the-fly navigation systems, and in agriculture to help regulate the application and use of fertilizers. Other uses for this ingenious system are being developed every day.

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