Problem 32.53 The GPS network consists of 24 satellites, each of which makes two

Question

Problem 32.53

The GPS network consists of 24 satellites, each of which makes two orbits around the earth per day. Each satellite transmits a 50.0?W (or even less) sinusoidal electromagnetic signal at two frequencies, one of which is 1575.42 MHz. Assume that a satellite transmits half of its power at each frequency and that the waves travel uniformly in a downward hemisphere.

Part A

What average intensity does a GPS receiver on the ground, directly below the satellite, receive? (Hint:First use Newton's laws to find the altitude of the satellite.)

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Part B

What is the amplitude of the electric field at the GPS receiver in part (a)?

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Part C

What is the amplitude of the magnetic field at the GPS receiver in part (a)?

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Part D

How long does it take the signal to reach the receiver?

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Part E

If the receiver is a square panel 1.00cm on a side that absorbs all of the beam, what average pressure does the signal exert on it?

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Part F

What wavelength must the receiver be tuned to?

Explanation / Answer

A) I = P/A

I = P / (2 pi R2)

I = ( 50 W) / (2pi * (2.66 * 107 - 6.38 * 106)2 )

I = (1.95 * 10-14 ) / 2

I = 9.75

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