GPS determines your distance from a satellite by measuring how long it takes an

Question

GPS determines your distance from a satellite by measuring how long it takes an electromagnetic wave to travel from the satellite to you. Imagine that a satellite is located at a distance of 127.2 km and is moving away from you at a speed of 12.0 km/s. (a) How long will it take an electromagnetic wave emitted by the satellite to reach you? (b) If the frequency of the wave emitted by the satellite is precisely 10.0 GHz, what is the frequency difference between this frequency and the frequency that you observe? SHOW EQUATIONS USED PLEASE!

Explanation / Answer

fo=fs(1+/-vrel/c) if vrel<<c

d=127.2km=127.2*103m
v=12km/s=12*103m/s
fs= 10GHz= 10*10^9Hz
c=3.00*108m/s

1)10.6 seconds
2)

f0=10*109 Hz (1-(12*103m/s/3.00*108m/s))=10*109 Hz

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