Nice question. It's not exactly the gravitational field that matters here but rather its integral, the gravitational potential. The sun is certainly at lower gravitational potential than the earth, so from our point of view it ages slowly. The magnitude of the effect is biggest near the middle of the sun and falls off a bit toward the outer part.
However, the effect is very small. You can estimate it from fraction GM/Rc
2, where G is the gravitational constant, M is the sun's mass, R is its radius, and c is the speed of light.
(published on 09/28/2010)
