# Telephone communications (easy question)

1. Feb 22, 2010

### Physics321

1. The problem statement, all variables and given/known data

Telephone connection between Europe and North America can be carried by cable or by the use of a geosynchronous communication satellite. Estimate the time it takes for a signal to travel 8000 km via cable, assuming the speed is close to the speed of light. How does this compare to the time required for the same signal to travel via satellite, at a near geosynchronous altitude of 40200 km from the center of Earth? (Assume the satellite is directly above the sending and receiving location of the signal.)

2. Relevant equations

time = (distance/speed)
so far I have the first part of this question correct, which asks 'estimate the time it takes for a signal to travel 8000 km.

3. The attempt at a solution

I have done this (8000 km x 1000 m)/(3E8 m/s) = 0.02666 seconds.
I am however confused on how to do the next part. It asks "how does this 'compare' to the time it takes for the same signal to reach 40200 km to a satellite".

Of course i first converted the km to m which would be 4.02E7 m. Am i suppose to find the time like above and somehow come up with a ratio?
Then, I would do something like this (4.02E7 m)/(3E8 m/s) = 0.134 seconds.
This is where i am stuck

I tried taking time1/time2 and time2/time1, but neither of these ratios work for the comparison

Any help would be appreciated.
Thank you.

2. Feb 22, 2010

### collinsmark

Don't forget the satellite link has a round-trip delay associated with it. The signal not only has to get from Earth to the satellite, it then also has to get from the satellite to Earth too.

Also according to the problem statement, the orbit is "40200 km from the center of Earth." It may be required that you subtract off the radius of the Earth to get the correct distance.

3. Feb 22, 2010

### Physics321

Oh that makes sense.

So in turn I understand that

2x(4.02E7 m) {for there and back} - (6.37E6 m) {for the radius of the earth} divided by the speed of light.

Hence [(2x(4.02E7 m))-(6.37E6 m)]/(3E8 m/s) = 0.2467 seconds.

Thus, I am still stuck on how to compare these two times

If I try the first method, I get 0.02666/0.2467 = 0.1080 {ratio}

Or if I try the second ratio, I would get (0.2467)/(0.02666) = 9.2535, which sort of makes sense.
This would mean that it takes 9.2535 times slower to go from Europe to North America using a satellite compared to using a cable? It sounds legitimate considering the distances.

4. Feb 22, 2010

### collinsmark

That's the right idea, except subtract off the radius of the earth before you multiply by 2.

5. Feb 23, 2010

### Physics321

Sure, that makes sense as well.

Thus:

[2(4.02E7 m-6.36E6 m)]/(3E8 m/s) = 0.2256 seconds

which makes the comparison as follows:

0.2256 seconds/0.02666 = 8.4621

which simply means,

It would take 8.4621 times longer to reach North America from Europe using the satellite method compared to using the cable method.

Thanks!