Does this mean that the people living on the space station age faster than people on earth, or does this only affect the atomic clocks?
The effect is a lot smaller in Low Earth Orbit. ISS is a mere ~423km above surface. GPS satellites are ~20,200km above surface. Here is the effect for different distances: http://en.wikipedia.org/wiki/File:Daily_satellite_time_dilat...
Relativity affects people as well as clocks.
It's not really valid to say simply that one is aging faster than the other as if one is doing something ordinary and one is doing something extraordinary. In this case, it really is relative. The people flying around in space are wondering what the hell you and your clock's problem is, too.
The rub is, time is relative, so even though your personal clock always reads 1 second in your own frame of reference, the clocks of two individual people in two different frame of references can disagree. So, it only really looks like the person in the space station "ages faster", but if both the people in both frames lived 100 years, they would be experience 100 years in their personal reference, but the space station guy might die when the earth guy is like 99.9999(or something, I didn't do the math here) years old.
This is due to gravitation time dilation, and it's not the only type. For instance if I went off on a super space ship at a very high fraction of the speed of light, traveled around the galaxy and returned 10 years later, situation would be reversed from the space station/earth gravitation scenario, and while 10 years may have passed ship time, many hundreds of years(once again, I didn't do the math, it's just more the higher fraction of the speed of light you are going) may have passed on earth. In this case, it is the accelerated frame of reference in which time "slows down" relative to the non-accelerated frame.
If you're talking about an object in orbit compared to an object at rest on the Earth's surface, both gravitational time dilation and the other type you describe come into play, because the objects are in motion relative to each other as well as being at different altitudes in the Earth's gravitational field. Many other comments in this thread have addressed this.
> In this case, it is the accelerated frame of reference in which time "slows down" relative to the non-accelerated frame.
Not really. The key difference is not acceleration; it's the fact that the super space ship is in motion relative to the center of mass of the galaxy, while the Earth is not. (Strictly speaking, the Earth is too, but its motion with respect to the galaxy's center of mass is so slow that it can be ignored in this scenario.) Similarly, if I sit at rest on the Earth's equator and you move westward around the equator at the same speed as the Earth is rotating (about 450 meters per second), then when we meet up again, my clock will have less elapsed time than yours, because you will have been at rest with respect to the Earth's center of mass, not me (because I am rotating with the Earth, but you are not).
In the spaceship and the earth example, I can't see what your reference of the galactic center of mass has to do with anything. If you take the space and earth out of the galaxy into empty space, the result would be very much the same. You could say there would be some slight differences because of the extremely minor differences caused by the gravitation effects of the galaxy and the acceleration due to galactic orbit, but being that relativistic speeds are require to see the big differences(we were talking about a spaceship capable of high fractions of C here), I can't see what you were getting at. It is the accelerated frame in which time is "slower" relative to the rest frame, it has nothing to do with gravity.
The galactic center of mass defines a reference frame that is special with respect to this problem, because that frame is the one that makes manifest the time translation symmetry of the spacetime. However, I do see that I left out an important piece of that: see below.
> If you take the space and earth out of the galaxy into empty space, the result would be very much the same
Yes, because empty space has a similar time translation symmetry, as long as the Earth is at rest in it. If the galaxy is included, the Earth has to be at rest relative to the galactic center of mass; I see now that I was implicitly assuming that it was, without saying so (I did hint at it when I commented about the Earth also rotating around the galactic center, but too slowly to make a difference). So you're right that the galaxy itself isn't really relevant; but the underlying time translation symmetry is.
The point is that what makes the Earth observer in these scenarios have the longest proper time is the fact that he is the one who is "at rest" with respect to the underlying time translation symmetry of the spacetime. Acceleration only comes into it because that is the particular mechanism you chose to make the space ship move relative to that time translation symmetry. In flat spacetime (which is essentially the idealization you're adopting here), accelerating is the only way to move relative to the underlying time translation symmetry. But this does not generalize: there are plenty of examples in curved spacetime where unaccelerated observers can be the ones with shorter elapsed proper time, because they are moving with respect to an underlying time translation symmetry.
The faster you move, the lesser "Time" needs to be in order to be equal to c.
But you got it backwards, they age slower.
Edit: or maybe not, now in am confused.
Traveling fast slows time down, and going closer to heavy object slows down time so if earth is heavy enough time would speed up by being in orbit. You are right, if that is the case.
There are two effects here.
First, gravitational time dilation slows the on board tick rate deep in the gravity well. As you get out of the well your on board tick rate increases relative to the surface due to decreasing strength of the gravitational field.
Second, motional time dilation slows the on board tick rate down as your velocity increases. This effect always slows the on board tick rate down and can never increase it relative to the surface. However, the magnitude of the affect decreases. As you move to higher orbit your orbital velocity decreases and so does the motional time dilation.
There are a few useful reference points which help to think about tick rate on board various satellites relative to the tick rate on the surface.
1. On the hypothetical orbit at altitude zero gravitational time dilation relative to the surface has no effect and tick rate slows down solely due to motional time dilation. On board tick rate is lower than for a stationary observer on the surface.
2. On the geostationary orbit motional time dilation has no affect (since relative velocity is zero) and tick rate increases solely due to reduced gravitational time dilation (we're further out the gravity well). On board tick rate here is higher than for a stationary observer on the surface.
3. Somewhere between these two extremes is an orbit where the two effects balance out and the on board tick rate is the same as the tick rate on the surface. This occurs roughly one half of Earth's radius (~3186km) up above the surface.
ISS is merely ~423km above the surface and so it's the tick-rate-slowing motional time dilation that matters and their clocks run slower from our point of view.
GPS is over 20,000km above the surface and it's the tick-rate-increasing effect of the reduced gravitational time dilation that matters so onboard tick rate is higher from out point of view.