I’m confused about the special relativity part. Wouldn’t the *orbiting* satellite be in a constantly accelerating reference frame, and not in constant linear motion away from / towards an observer?

Is it possible for the special relativistic effects to even accumulate; wouldn’t it “un-do” the effects on the second half of an orbit?

Thanks for posting. Indeed, the resolution power of the GPS satellites depends on the precision of clocks. It is my understanding that, roughly speaking, precision to 1 nanosecond translates to about a foot of precision (the speed of light is very close to one foot per nanosecond). So to be off 38 microseconds per day amounts to the satellites being off by about 38,000 feet per day, or just over 7 miles! The more and more accurate we make our clocks, the more and more accurate GPS systems can become.

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Twin_paradox

The size of the effect is irrelevant to whether this is a “good” example of the effect of both SR time dilation and the GR correction term, both separately and together. What makes it “good” is that both the space and ground based clocks are exceptionally accurate and stable so the signal (38 micro s) is tested to very high precision. An error of that scale corresponds to some huge position error on earth, so it had better be right.

As I understand it, the first GPS satellite could be switched between the desired ground frequency and the frequency required for it to work if relativity was correct. (Apparently, as the story goes, there were some unconvinced folks in the Air Force.) It did, and this makes it an actual twin experiment that, because the speed is so much higher than in the cases studied using aircraft, does show the effect for those “twin” clocks very clearly.

Of course, Dr. Pion knows all about the importance of time dilation when trying to transport a pion from its production area, through a target, and on through a magnetic spectrometer. Experiments with pions and muons were the first tests of the time predictions of SR.

Thanks for the reply.

Relativity does very strange things. It had brought to my attention that spheres remain spheres under the transformation!

In response to your question, this may be something like what you’re looking for. It’s free, there are lots of objects to be imported, and you can make your own shapes from external programs.