Time Dilation: Impact on GPS Accuracy

[nordqvist11]

Hey there guys I just have a question to ask some of you. Given the occurrence of time dilation being related to an objects state of motion I have an interesting thought.

This is a very general question, my teacher only briefly covered this topic in class as it's not part of our course but it intrigued me. If I am traveling at a speed of .99 C in a plane around the Earth and I am hooked up to a GPS which shows me my location on the map in my plane, relevant to my position in an instantaneous moment would the GPS be precise?

 

[Trevormbarker]

I think you mean time dilation? I have never heard of time distillation before. And I believe yes but someone correct me if I am wrong

 

[bahamagreen]

Your plane will be circling the Earth about eight orbits per second...
To do that your plane will need to point almost to the center of the Earth and your direction of motion will be almost perpendicular to the floor of the plane in the cabin roof direction ("up" from your seat).
This will make for some peculiar effects:
A phenomenal G force directed to the rear of the plane ("back" into your seat).
An orbit frequency making GPS too fast to read by eye
Length contraction of the Earth in the vertical (floor to ceiling) corresponding to the latitudinal direction of the Earth (if your plane is in an equatorial orbit).
Also, if you used a high speed camera or computer link to read the GPS display, the delay in transmission of signal would be a not insignificant contribution to measurement error.

But all these things aside, as a thought problem, I think the actual GPS system is supposed to work in theory even under these extremes.

 

[Janus]

Hey there guys I just have a question to ask some of you. Given the occurrence of time dilation being related to an objects state of motion I have an interesting thought.

This is a very general question, my teacher only briefly covered this topic in class as it's not part of our course but it intrigued me.


If I am traveling at a speed of .99 C in a plane around the Earth and I am hooked up to a GPS which shows me my location on the map in my plane, relevant to my position in an instantaneous moment would the GPS be precise?

No. For one, a normal GPS would likely not even work. Your high velocity with respect to the satellites would cause a large Doppler shift in the signals to the point that would your GPS receiver would not pick them up.

Secondly, Your receiver clock would be running much slower than the GPS clock. Since calculation of position requires a comparison between receiver clock and the time index it receives from the satellite and then using difference between these times and the speed of light to tell how far the receiver is from the satellite, and this requires both clocks to run at the same rate, you would not get an accurate answer.

and Third, even if you corrected for this time rate difference, by the time you got the information that you were x kilometers from satellite n, the information would be obsolete. It would take a minimum of .067 sec for the signal to reach you, by which time you will have moved almost 20,000 km, or ~1/2 the way around the world.

 

[nordqvist11]

No. For one, a normal GPS would likely not even work. Your high velocity with respect to the satellites would cause a large Doppler shift in the signals to the point that would your GPS receiver would not pick them up.

Secondly, Your receiver clock would be running much slower than the GPS clock. Since calculation of position requires a comparison between receiver clock and the time index it receives from the satellite and then using difference between these times and the speed of light to tell how far the receiver is from the satellite, and this requires both clocks to run at the same rate, you would not get an accurate answer.

and Third, even if you corrected for this time rate difference, by the time you got the information that you were x kilometers from satellite n, the information would be obsolete. It would take a minimum of .067 sec for the signal to reach you, by which time you will have moved almost 20,000 km, or ~1/2 the way around the world.

Really great stuff, thanks a lot.