Effect of Einstein's Theory of Relativity on GPS

[jimh]

I was listing to an interview with an astro-physicist being broadcast on the radio a few days ago. Regarding a question of how astro-physics affects everyday life, she cited the instance of the Global Positioning System. Were it not for consideration of Einstein's Theories of Relativity, she said, the position accuracy of GPS would be no better than about six miles. This startled me a bit, as I did not think the error would be so large. I searched for another opinion. The radio-interviewee's opinion was confirmed by an article I found called Real-world Relativity: The GPS Navigation System. The author is a professor of Astronomy at Ohio State University.

I found this example of space-time relativity to quite interesting. I did not realize that the accuracy of GPS position solutions depended upon making compensation for such effects. Perhaps other readers will enjoy the brief summary of the influences. I found it a very interesting read. The article contains may hypertext links to more material about this phenomenon.

[porthole]

H'mmm. [The linked article revealed to me that] two concepts of GPS I had were wrong. Now I find out that the satellites have a built in intentional error just so those of us on earth can get an accurate position calculation.

[And also found out the orbits of the] satellites are not geostationary, and [found out that the GPS] uses trilateration and not triangulation.

[jimh]

I think you misunderstand what has occurred. There is no "intentional error" in the design of the Global Positioning System satellites. The more one studies the intricacies of the GPS, the more one comes to marvel at the fantastic skill in science, math, engineering, and production that was necessary to bring GPS into being. The notion that the cost of a GPS receiver has decreased from several hundred thousand dollars to perhaps less than a dollar is also fantastic. The overwhelming majority of the one-billion users of GPS have no concept of any of this. They just say, "Siri, where is the nearest Starbucks?" and I don't think they appreciate the enormous engineering skill that makes all of that possible.

[porthole]

Maybe error is a poor choice, I was referring the the intentional time offset so ground based receivers match the times of the SATs

[jimh]

The time clocks on satellites in the GPS constellation are not "offset" in time. The clock rate of the satellite's atomic clocks has been altered slightly compared to how the clock would run if on Earth and stationary. As the article [linked in the initial post] mentioned, the altered clock rate is to account for the composite effects of Einstein's Theories of Relativity regarding how the clocks would appear to a stationary user on Earth.

The actual time kept by GPS satellites is not in UTC. Their clocks are never reset for the usual leap-second that is added to UTC periodically. When a GPS receiver displays the time to the user, it takes the GPS time and applies the appropriate offset from UTC. The satellites transmit the offset from UTC as part of their data to the user-segment. I think the offset right now is about 15-seconds.

For more interesting information about time keeping on the GPS satellites, see an earlier article at

http://continuouswave.com/ubb/Forum6/HTML/003088.html

[jimh]

The effect of time dilution on a clock that is moving with respect to a stationary observer was tested in 1971 in what is known as the Hafele–Keating experiment. Atomic clocks were flown around the world on commercial airliners, and their time compared to an identical stationary clock. This is recounted briefly in a very interesting article in Wikipedia.

[porthole]

Maybe error is a poor choice, I was referring the the intentional time offset so ground based receivers match the times of the SATs

a) The time clocks on satellites in the GPS constellation are not "offset" in time.
b)The clock rate of the satellite's atomic clocks has been altered slightly compared to how the clock would run if on Earth and stationary.
c) The satellites transmit the offset from UTC as part of their data to the user-segment. I think the offset right now is about 15-seconds.

So which is it?
A
B
C

or, none of the above?

[jimh]

ASIDE to Porthole: Your question imposes a condition on the answer which does not exist. You seem to think that the three statements are somehow exclusionary or else are all false. They are not exclusionary, and all three statements are true. This makes your question unanswerable in the constraint you applied.

Time in GPS satellite clocks is not maintained at any fixed offset from any other clock or time. (Your "A" inquiry.)

The satellite clock rates have been altered so they appear synchronous with stationary clocks to a stationary observer of the satellite. When two clocks appear synchronous they have the same time, that is, there is no offset in time. (Your "B" inquiry.)

GPS satellite clock time does not pay attention to UTC leap seconds. A GPS receiver applies an offset to GPS time so it can tell the user of the GPS receiver what the UTC time is based on how far off the UTC time is from the GPS clock time. The clocks in the satellites pay no attention to UTC and run with their own time reference epoch. (Your "C" inquiry.)

I recommend you read more about GPS to understand better how it works. May I suggest this book:

Global Positioning System:
Signals, Measurements, and Performance
Revised Second Edition (2011)
By Pratap Misra and Per Enge
http://www.gpstextbook.com/

The authors have very nicely provided an on-line preview of Chapter 1, which may be enlightening.

[jimh]

For more discussion about the relativistic effects on GPS, here are pages and pages of articles from a GOOGLE search. Perhaps the most concise is from Wikipedia.

[jimh]

I was re-reading this thread this morning, and I noted something interesting in my initial posting. I said:

I was listing to an interview with an astro-physicist being broadcast on the radio a few days ago. Regarding a question of how astro-physics affects everyday life, she cited the instance of the Global Positioning System.

This observation is, in itself, worth remarking, that is, that use of the Global Positioning System is now a part of everyday life. There are more than one-billion people making use of GPS every day. When GPS receivers first became affordable, their use in marine navigation represented a significant percentage of the user-segment. Today, use of GPS in marine navigation is but a very tiny sliver of the total user-segment. GPS technology has truly become part of everyday life.