How does gravity affect time dilation? I understand that the faster you move through space the slower you move through time, but how does gravity play a role in that?
 A: Gravitation is an effect due to the curvature of spacetime. Both space and time are curved by the presence of matter (and other energy). One manifestation of the curvature is time dilation: time passes more slowly for someone close to a heavy mass than for someone far away. This isn't just a theoretical effect, it's easily observed by modern atomic clocks. For example, if you place two identical atomic clocks on different floors of a building, the higher one will gain time relative to the lower one. The difference is a matter of nanoseconds per week (or less) but it is measurable.
The time dilation due to gravity is related to the time dilation due to different speeds by an interesting formula: a clock that is "stationary" in a gravity well (e.g. on the surface of the Earth) runs slow relative to a distant stationary observer by the same amount that a clock moving at escape velocity would. The deeper you are in a gravity well, the higher the escape velocity from that point, and hence the greater the time dilation.
