“If you calculate out the motions of the sun, and earth, the gravitational effects you feel from the sun (this effects where the earth is in its orbit amongst other things), the sun is not in the position it ought to be by virtue of the gravity we feel from it.”
If I’m understanding you correctly, you mean that the apparent visual position of the sun (transmitted by the light) is different from its actual position, deduced from gravitational effects. That alone demonstrates nothing, since it does not mean that any actual “motion” of gravity has occcurred, and without even being able to demonstrate motion, you can’t hope to make any conclusions about the velocity.
In fact, if gravity worked the way you propose, it would have to have an infinite velocity, since its effects are instantaneously apparent at any distance (if you can detect them). Anything with an infinite velocity would also have to be ever present in every location in the universe equally, so we would all experience the exact same gravitational effects as everywhere else. Since that is not the case, then it is apparent that gravity can’t work that way.
Actually, infinite velocity is exactly what it implies IMO. I don't see how it would follow that we would all experience the exact same gravitational effects as everywhere else. Gravitational effects are still bound by distance. Not inverse square, thankfully, but the effect lessens with distance, though in theory every single particle, no matter how separated by distance does have some effect on each other gravitationally.
I can't remember exactly where I first read about the discrepancy between the sun's apparent position and it's gravitational effect, as it was some time ago. I think it was a freeper who pointed it out to me, but I get old and forgetful. I'll do some searches on this tonight, if I'm not distracted by shiny things.
The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c.[1] Within the theory of special relativity, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space.[2] This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any massless particle. Such particles include the gluon (carrier of the strong force), the photons that light waves consist of, and the theoretical gravitons which make up the associated field particles of gravity (a theory of the graviton requires a theory of quantum gravity, however).
The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field, because of relativistic considerations, are the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.
The consequence of this, is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.