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If one of the GP satellites is at a distance of 19,000 km from you, what percent...

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fushi | (Level 1) Valedictorian

Posted August 28, 2013 at 4:31 PM via web

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If one of the GP satellites is at a distance of 19,000 km from you, what percent accuracy in the distance is required if we desire a 2 meter uncertainty and how many significant figures do we need to have in the distance?

Global positioning satellites (GPS) can be used to determine positions with great accuracy. The system works by determining the distance between the observer and each of several satellites orbiting Earth.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 28, 2013 at 4:45 PM (Answer #1)

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Global positioning satellites are used to determine position with great accuracy. If the distance of a global positioning system from 4 satellites is known and the exact position of the four satellites being used is known, the position of the system including altitude can be estimated.

The distance of one of the satellites is 19000 km. If it is required to know the position with an uncertainty of only 2 m, the distance can therefore lie between 19000.002 km and 18999.998 km.

The acceptable error in the distance is given by `(|19000 - 19000.002|/19000.002)*100` = 1.05*10^-5 %.

The number of significant figures required in the distance is 8.

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