# How long will it take an electromagnetic wave to reach a satellite

## Homework Statement

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 127.2km and is moving away from you at a speed of 12.0km/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?

## Homework Equations

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

## The Attempt at a Solution

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

Part A: 10.6 seconds
Part B:

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

Dick
Homework Helper

## Homework Statement

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 127.2km and is moving away from you at a speed of 12.0km/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?

## Homework Equations

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

## The Attempt at a Solution

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

Part A: 10.6 seconds
Part B:

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

For Part A, don't you think the time will have rather more to do with the speed of light than the speed of the satellite? For Part B, don't you think keeping more accuracy in the answer might be useful?

rude man
Homework Helper
Gold Member
In addition to the problems pointed out in post #2 you have the wrong formula for the Doppler shift.

It's based on the theory of relativity so don't try to derive it. Look it up.

Dick
Homework Helper
In addition to the problems pointed out in post #2 you have the wrong formula for the Doppler shift.

It's based on the theory of relativity so don't try to derive it. Look it up.

Depends on how much accuracy you need. It certainly doesn't matter if you round to the nearest GHz, like aChordate. But if I use the nonrelativistic formula and compare the results with the relativistic the frequency shifts are the same to 4 decimal places.

rude man
Homework Helper
Gold Member
Depends on how much accuracy you need. It certainly doesn't matter if you round to the nearest GHz, like aChordate. But if I use the nonrelativistic formula and compare the results with the relativistic the frequency shifts are the same to 4 decimal places.

I doubt that the OP was aware of that. In any case, he/she might as well use the correct formula in case a future problem involves speeds closer to c.

EDIT: I have to admit that, if the emphasis was on satellites, the OP might never encounter the relativisic formula, so on second thoughts I think you were right to point out what you did.

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