Both are at play.
Quote:
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.
For instance, two rocket ships (A and B) speeding past one another in space would experience time dilation. If they somehow had a clear view into each other's ships, each crew would see the others' clocks and movement as going too slowly. That is, inside the frame of reference of Ship A, everything is moving normally, but everything over on Ship B appears to be moving slower (and vice versa).
From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate. In other words, if a new ship, Ship C, travels alongside Ship A, it is "at rest" relative to Ship A. From the point of view of Ship A, new Ship C's time would appear normal too.[4]
A question arises: If Ship A and Ship B both think each other's time is moving slower, who will have aged more if they decided to meet up? With a more sophisticated understanding of relative velocity time dilation, this seeming twin paradox turns out not to be a paradox at all (the resolution of the paradox involves a jump in time, as a result of the accelerated observer turning around). Similarly, understanding the twin paradox would help explain why astronauts on the ISS age slower (e.g. 0.007 seconds behind for every 6 months) even though they are experiencing relative velocity time dilation.
Quote:
Gravitational time dilation is at play for ISS astronauts too, and it has the opposite effect of the relative velocity time dilation. To simplify, velocity and gravity each slow down time as they increase. Velocity has increased for the astronauts, slowing down their time, whereas gravity has decreased, speeding up time (the astronauts are experiencing less gravity than on Earth). Nevertheless, the ISS astronaut crew ultimately end up with "slower" time because the two opposing effects are not equally strong. The velocity time dilation (explained above) is making a bigger difference, and slowing down time. The (time-speeding up) effects of low-gravity would not cancel out these (time-slowing down) effects of velocity unless the ISS orbited much farther from Earth.
The key is that both observers are differently situated in their distance from a significant gravitational mass. The general theory of relativity describes how, for both observers, the clock that is closer to the gravitational mass, i.e. deeper in its "gravity well", appears to go slower than the clock that is more distant from the mass. This effect is not restricted to astronauts in space; a climber's time is passing slightly faster at the top of a mountain (a high altitude, farther from the Earth's center of gravity) compared to people at sea level. As with all time dilation, the local experience of time is normal (nobody notices a difference within their own frame of reference). In the situations of velocity time dilation, both observers saw the other as moving slower (a reciprocal effect). Now, with gravitational time dilation, both observers—those at sea level, versus the climber—agree that the clock nearer the mass is slower in rate, and they agree on the ratio of the difference (time dilation from gravity is therefore not reciprocal). That is, the climber sees the sea level clocks as moving slower, and those living at sea level see the climber as moving faster.
Emphasis mine. The altitude/speed are both factors so I snagged them for the ISS (whats mentioned in this article)
7,706.6 m/s, apogee is 424,000 meters, perigee 402,00 meters.
and for a geostationary orbit (note that geostat orbits are much larger than most)
~3,070 m/s and an altitude of ~35,786,000 meters
I should note that the GPS constellation doesn't fly in geostat orbit, but about half that IIRC.
I am aware that both are at play, but the whole point of the original post was simply to draw issue with the statement that you didn't have to compensate for relativistic effects before a significant fraction of
cEdit: Just a little more data, just because I finally found it--GPS orbits are about 26,600,000 km, with an orbital period of just under 12 hours.
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