(republished on 07/23/06)
What you seem to be describing is the theory of General Relativity. According to GR, if two clocks are placed in a gravitational field with one being deeper in the field than the other, the time will not pass at the same rate for each clock. The clock that is farther away from whatever is causing the gravitational field will measure time to be passing faster than the clock that is closer to the massive object causing the field. This comes from the effect that gravity has on the passage of time, and not that it affects the mechanics of clocks specifically, of course. This is called time dilation.
Your question about the speed of time though is a bit difficult to understand. If your asking whether time travels at a certain speed through space, then the answer would be no. Time does not travel through space at a finite speed like light or an object that has been thrown. If two clocks were synchronized, at rest with respect to each other and were not in any gravitational field, the two clocks would read the same time no matter how far apart they were.
We also know that time isn't concentric with the universe because the universe has no center, nor did the Big Bang take place at a specific location. The Big Bang was an explosion of space, not an explosion in space. Our observations indicate that the universe is both homogeneous and isotropic, meaning that (on large scales) the structure of the universe is uniform and the same in all directions. There's no indication that any place is more the center than any other place.
(published on 04/23/13)