The Global Positioning System (GPS) uses a \"constellation\" of some 30 satellit

Question

The Global Positioning System (GPS) uses a "constellation" of some 30 satellites to provide accurate positioning for any point on Earth, as given in the figure. GPS receivers time radio signals traveling at the speed of light from three of the satellites to find the receiver's position. Signals from one or more additional satellites provide corrections, eliminating the need for high-accuracy clocks in individual GPS receivers. GPS satellites are in circular orbits at 20,200 km altitude.

What's the approximate speed of GPS satellites?

Explanation / Answer

The gravitational force on GPS satellites which equals to the centripetal acceleration.

using a formula, we have

V = sqrt(GM/(R + h))

M = mass of earth = 5.98 x 1024 kg

R = radius of earth = 6.37 x 106 m

h = height above surface of earth = 2.02 x 107 m

V = sqrt((6.67 x 10-11) (5.98 x 1024)/((2.02 x 107) + (6.37 x 106))

V = 3874.52 m/s

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