The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites or

Question

The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using "triangulation" and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of the six orbits, allowing continuous navigational "fixes." The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile = 1.852 km = 6076 ft].

(a) Determine the speed of each satellite.
m/s

(b) Determine the period of each satellite.

Explanation / Answer

a)

to move in circular orbits, the satellites must have a centripetal acceleration.

And that acceleration s provided by the acceleration due to gravity

So, g = v2 / R ; where R is the altitude of the satellites.

v = sqrt (Rg) = sqrt (1852 * 9.8) = 134.72 m/s

b)

Period of the satellite means the time taken in orbiting the earth.

T = 2 (pi) R / v = 2* pi* 1852 / 134.72 = 86.375 seconds

So, period of each satellite is 86.375 seconds

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