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gravity is one of the fundamental forces of the universe and frankly we just DON'T understand it. we can explain it and demonstrate it using analogy and examples... but your asking why, and no one knows why.... it just "does" warp space-time. You aren't going to get a "logical" explanation to "why" something in physics happens or exists. It isn't a "logical" process. Existence exists despite our logical failures to explain it. The acceleration part should be obvious to anyone who is living on a planet with gravity... as things fall, they speed up and fall faster over time. Of course the sun is moving, it both rotates around its axis and revolevs around the galaxy.

I'm afraid that it is necessary to understand at least a little about a subject before you can ask a sensible question about it. You appear to understand nothing.

The is no answer to WHY massive objects warp space-time. They just do. Science observes and describes what happens, it does not have anything to say about why it happens.

Acceleration and gravity have the same effects. You can observe one of the effects of acceleration by riding in an elevator. Going up, your weight apparently increases - just the same feeling as if gravity momentarily increased. Going down, your weight decreases - the same feeling as if gravity momentariy decreases. If you did not know that the lift was moving, there would be no way for you to decide which was the true cause - is the lift moving, or is gravity increasing / decreasing? The effects of both are the same, there is no way to differentiate one from the other.

Ok, I know this seems very complicated; but thats because it is :P. There are alot of things to consider simultaneously.

Gravity IS an acceleration. Any object of mass has a gravitational pull, this is something we (or at least I) don't completely understand.

I can't explain why massive objects drag on time, but I believe it has to do with e=mc^2 if I remember correctly. But I can easily explain our orbit relative to the sun.

The sun and other stars are the most massive things in the universe besides black holes. Even the sum of all of the masses of the planets surrounding our sun are negligible compared to the mass of the sun itself. So even though the sun may move, its motion is imperceptible compared to the motion of the planets around it. Consider the universal gravitational force equation: F=GMm/r^2. Where M is the larger mass and m is the smaller mass; r is the position vector from M to m and G is the gravitational constant. When this force is applied to each individual planet relative to the sun, the acceleration: a=F/m=GM/r^2 (M is the mass of the sun) is relatively large, so the planets have large orbits. But when all of the forces of the planets on the sun are summed up and then the overall effect is considered, we're left with a=G(m1 +m2+m3...+m9)/r^2; where m1...m9 are the masses of the planets. This acceleration is actually relatively small, so the sun doesn't move much.

I know this is a bit confusing and I didn't give the best explanation, but I advise taking a couple of college level physics courses if you really want to understand... I've apparently forgotten some of the theory since mine :(

Edit: I also meant to mention that there are galaxies with two central stars (suns), called binary star galaxies, in existence; and these suns exhibit very interesting orbits around each other (really around one central point which is the center of mass of the two-mass system). Since we are dealing with two masses more near each other in magnitude, the motion of each star is much more dramatic than a one star galaxy. If you're interested in astronomy, you should definitely look this up.

You mix all things together.No need take for understanding these very big objects.All objects moving in time but whom with acceleration are not visible.All objects that is moving with acceleration change color first and after to be invisible(between you and them there are space with other bodies).Other time mean other space.

When you decide what example we might use to help with your questions, be sure and let us know. Asking a question and then placing restrictions on the type of answers that may assist your understanding is max foolish.

NOTE:

The sun does move -- it circles our galaxy at about 250 km/sec, and it rotates on its own axis.