# Global positioning system (GPS)

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Case study notes[1]

## Introduction

The Global Positioning System (GPS): was designed for military applications. Its primary purpose was to allow soldiers to keep track of their position and to assist in guiding weapons to their targets. The satellites were built by Rockwell International and were launched by the U.S. Air Force. The entire system is funded by the U.S. government and controlled by the U.S. Department of Defence. The total cost for implementing the system was over \$12 billion.

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Presently the system is right now open for everyone to use it. The only condition is to have a GPS device for e.g.

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A GPS satellite:

The GPS constellation of satellites consists of at least 24 satellites – 21 primary satellites and 3 orbiting spares. They orbit the earth at an altitude of 17,500 km at a speed of 3.06 km per second between 60°N and 60°S latitude. Each satellite weighs 861 kg and is 5.81 meters wide with solar panels extended. The satellites orbit the earth twice a day. This guarantees that signals from six of the satellites can be received from any point on earth at almost any time. The global coverage is 24 hours a day, all weather conditions.

## How does it work

The position of a user is calculated by measuring the distance to three/four satellites, taking the point of intersection in a process called trilateration. In order for this to work, each satellite carries an atomic clock so that the distance between the GPS receiver and the GPS satellite can be calculated through exact time differences.

Trilateration: Imagine you are standing somewhere on Earth with three satellites in the sky above you. If you know how far away you are from satellite A, then you know you must be located somewhere on the red circle. If you do the same for satellites B and C, you can work out your location by seeing where the three circles intersect. This is just what your GPS receiver does, although it uses overlapping spheres rather than circles.

The more satellites there are above the horizon the more accurately your GPS unit can determine where you are.

GPS and Relativity: GPS satellites have atomic clocks on board to keep accurate time. General and Special Relativity however predict that differences will appear between these clocks and an identical clock on Earth. General Relativity predicts that time will appear to run slower under stronger gravitational pull – the clocks on board the satellites will therefore seem to run faster than a clock on Earth. Furthermore, Special Relativity predicts that because the satellites’ clocks are moving relative to a clock on Earth, they will appear to run slower. The whole GPS network has to make allowances for these effects – proof that Relativity has a real impact.

## Examples

Your imagination is the only limitation to the possibilities of global positioning system (GPS) technologies. GPS systems are extremely versatile and can be found in almost any industry sector. They can be used to map forests, help farmers harvest their fields, and navigate airplanes on the ground or in the air. GPS systems are used in military applications and by emergency crews to locate people in need of assistance. GPS technologies are often working in many areas that we do not normally consider.

Global positioning system applications generally fall into 5 major categories:

1. Location - determining a position

2. Navigation - getting from one location to another

3. Tracking - monitoring object or personal movement

4. Mapping - creating maps of the world

5. Timing - bringing precise timing to the world

## Extra informations

NovAtel Inc. is a leading provider of precise global positioning system and augmentation technologies designed to afford its customers rapid integration and exceptional return on investment.