The GPS network consists of 24 satellites, each of which makes two orbits around

Question

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. ( 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.) ( b) What are the amplitudes
of the electric and magnetic fields at the GPS receiver in part ( a), and how long does it take the signal to reach the
receiver? ( c) What wavelength must the receiver be tuned to?

Explanation / Answer

A- I =9.75×10-15 W/m^2 Because I=P/A >>> I = P/2pi R^2 so I = (50W)/(2pi*(2.66*10^7 - 6.380*10^6)^2 this will give I = 1.95*10^-14 Then Divide By 2 To get I =9.75×10-15 W/m^2 B- =2.71×10-6 N/C Because Emax = sqrt(2 * M0 * C * I) Emax = sqrt ( 2* (4pi *10^-7 * 3*10^8 * 9.75*10^-15) So = 2.71×10-6 N/C C- =9.03×10-15 T Bmax = Emax/C = 2.71*10^-6/(3*10^8) so Bmax = 9.03×10-15 T D- =6.73×10-2 s time = (Radus of earth)/speed =(26601.286 - 6380)/3*10^8 = 6.73×10-2 s E- =3.25×10-23 Pa P= I/C P = (9.75*10^-15)/(3*10^8) p = 3.25×10-23 Pa F- =0.190 m wavelength = c/f = (3*10^8)/1575.42*10^6 =0.190 m

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