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The Global Positioning System satellites operate at an altitude of 20,200 km and use communication frequencies of 1575.42 MHz. Find the gravitational frequency change with respect to Earth.

The Global Positioning System satellites operate at an altitude of 20,200 km and use communication frequencies of 1575.42 MHz. Find the gravitational frequency change with respect to Earth.

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The Global Positioning System satellites operate at an altitude of 20,200 km and use communication frequencies of 1575.42 MHz. Find the gravitational frequency change with respect to Earth.

Expert Solution
Step 1

Given data, h=20,200 (km);

frequency, f=1575.42 (MHz);

So, with respect to earth gravitational frequency change for an altitude h is given by the equation;

∆f=-GMc21R+h-1Rf................................1

also for the above equation, we know the value of some constants as;

Gravitational constant,  G=6.67×10-11 Nm2/kg2;

Mass of the Earth,  M=5.976×1024 kg

The radius of the Earth,   R=6.37×106 m

The velocity of light,  c=3×108 m/s

now putting all the value in the equation (1) we get;

∆f=-GMc21R+h-1Rf∆f=-6.67×10-11 Nm2/kg2×5.976×1024 kg3×108 m/s216.37×106 m+20200 km-16.37×106 m1575.42 MHz=0.00346 Hz

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