A friend just sent me some viewgraphs from a presentation that he recently attended on the history of the Global Positioning System (GPS). The presentation was given by Hugo Fruehauf, one of the key GPS developers. In this presentation, he discussed the effect of relativity on GPS timing accuracy. I thought the following graph was worth discussing here.
This presentation initiated a number of interesting discussions at work. The most interesting question was why do general relativity and special relativity introduce errors of opposite sign? Here is my take on the subject.
- General relativity
This introduces a positive frequency error because a clock on earth is subject to a stronger gravitational field than the satellite. This means that the clock on earth will run slower than the clock on the satellite. Stated another way, the clock on the satellite will run faster than the same clock on the earth.
- Special relativity
This introduces a negative frequency error because a clock on the satellite is moving relative to the same clock on the earth. This means the clock on the satellite appears to run slower than the same clock on earth.
In my engineering career, I have only encountered relativistic effects once before. That was with modeling the behavior of fast-moving electrons in a cathode-ray tube (CRT). The increase in the mass of an electron after being accelerated by the electron gun needed to be accounted for during the design of a graphics display system.