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Circles in the Coordinate Plane

Standard equation based on center and radius.

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GPS Geometry

Credit: NASA
Source: http://en.wikipedia.org/wiki/File:GPS_Satellite_NASA_art-iif.jpg
License: CC BY-NC 3.0

Ever wonder how your cell phone or car navigation system always knows exactly where you are? It seems like magic, but the core of global positioning system (GPS) technology lies in satellite communication and geometry.

Why It Matters

In very simple terms, GPS technology allows a device on the Earth’s surface to determine its position as it relates to the intersection of multiple circles. Think about your location as a point on a coordinate grid, and imagine three satellites as other points anywhere else on the grid. Say the first satellite figures out that you are 5 units away, but doesn’t know in what direction. The second and third satellites figure out that you are 6 and 7 units away, respectively, but they also don’t know in which direction you’re located—only that you’re a fixed distance away. By drawing three circles, with each satellite as a center and the respective radii 5, 6, and 7 units, the three circles would intersect exactly where you are on the grid!

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

The picture above is a simplified illustration of how this happens with real GPS technology. The process is called trilateration. So how do the satellites figure out what distance, or radius, they are from your location? With a little physics, your mobile device uses the following information to determine your distance from a satellite: the time the satellite sent a signal, the time it was received on Earth, and the speed of light. Keep in mind that a coordinate grid and the illustration above are two-dimensional models. Real GPS navigation calculates the intersection of three or more spheres in three-dimensional space.

See for yourself: http://www.youtube.com/watch?v=PLjld-edVj8

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Learn more about position determination with GPS technology using the link below.


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Image Attributions

  1. [1]^ Credit: NASA; Source: http://en.wikipedia.org/wiki/File:GPS_Satellite_NASA_art-iif.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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