At different positions in its orbit, a GPS satellite will have differing speeds relative to different GPS receivers. Given this, do we need to adjust the speed used in the equation for time dilation to account for this variation?
That’s because, the velocity is relative to the earth as a whole, not to any fixed point. The earth rotates slower at the poles than at the equator so the exact velocity of the receiver will vary depending on where it is. Not to mention that more often than not the receiver itself will be moving. The relative velocity between the receiver and the satellite changes because the velocity of the receiver changes depending on location and/or speed…not because the velocity of the satellite changes.
Hi Pricelesspearl
I think the effects of time dilation are the same for all receivers on the surface of the Earth (at sea level), as all clocks at sea level tick at the same rate regardless of their rotational speeds. For example an observer at the north pole will feel stronger gravity than an observer at the equator, so the north pole observers clock should tick slightly more slowly. However, the observer at the equator has a faster rotational speed which cancels the effects and thus both observers clocks tick at the same rate.
Obviously not everyone lives at sea level and not everyone travels in a vehicle at the same speed, but i think the effects of time dilation due to this is very, very small.