Not being a GR expert, I may slightly falter in explaining the equations of this calculation. However I am confident that the result is correct if the correct jargon can be found. The essential point is that gravity affects radiation (and probably also the relativistic content of matter) by a greater amount than it affects non-relativistic matter. I believe that the correct proportion is 5/3 times as much when summed over all possible directions, being 2x in the four directions that are transverse to the direction of the body that causes the gravity and 1x in the two directions radially.

In a following post I will deal with the equations of momentum transfer. For now I will show that the effects are of sufficient magnitude to be a factor in solar output variations and possibly the magnetic field effects.

Horizontal radiation is bent 2x as much as in Newtonian gravity as predicted by Einstein and as measured. For a light ray that just skims the Sun's surface the effect is measured as 1.75" as against Newtons 0.875". Change of direction for light represents change of the momentum vector. If a light ray in the Sun is traveling transversely to Jupiter's direction, then it will be bent at a rate that is 1/1000* 1/1000^2 as fast as a light ray passing the Sun. The first 1000 factor results from the fact that Jupiter is that much less massive than the Sun. The additional two factors come from the fact that Jupiter is 1000 times as far away from the Sun as the Sun's surface is from its core. So we find that light in the Sun's core is being bent at a rate that is a billionth of the rate that it gets bent as it passes the Sun. An that was a tiny 1.75" of arc. So we are now down to about 0.0000000017" of arc bending. But it is not zero. :-)

There are some extra factors to reduce the result of that tiny effect. At any one time the radiation content of the Sun is something like 1 part in 10^7 of its total mass or energy content. See http://www.bautforum.com/questions-a...s-surface.html So when we are considering the difference in acceleration of the photonic content in the solar core (where the proportion is this 1 part in 10^7) and the surface where it is vastly less, the resulting acceleration will be about another 7 orders of magnitude less. We now have 0.00000000000000017" of arc bending each few seconds. The few seconds comes from the time that a photon is near the Sun in the famous Eclipse experiment.

Now we are almost ready to start on the the other side of the equation. There is one more factor to divide by, one more order of magnitude, due to the fact that the gas giants orbit at an angle of about 7 degrees to the Sun's equator. So they can spend long periods N or S of that equator. When they are N of the equator, the extra acceleration of the planet on the interior is towards the Planet, but then the Sun is rotating and so 13 days later most of the acceleration is undone by the same planet. However the component in the N or S direction is not undone. That component is about 1/10th. So the final figure for the extra acceleration on the internal part of the Sun per few seconds is 0.000000000000000017" of arc bending.

So what is the other side of the equation that could possibly compete with all those zeros? The answer is that the acceleration of the core of the Sun in a N or S direction by say Jupiter takes place in the same direction for 6 years at a time. Unlike the bending of light during an eclipse when the main action takes about 6 seconds. The equation for how far something gets moved by a constant acceleration is s = 1/2 a t^2 although in both cases the acceleration is not constant, rising from zero to a maximum and then falling away to zero again. However the proportion is correct. The effect of Jupiter is for a period about 30,000,000 times longer and due to the t^2 factot, the result in terms of actual movement is 10^15 times as much. So we take our little 0.000000000000000017" and knock 15 zeros off it and get 0.017" which is no longer quite so tiny. If we express this in radians it is about 10^-7 radians now something measurable.

Actually we can calculate the morion of the solar interior by a simpler more obvious means. Due to the outer planets the Sun moves about the COM by something like its own size over periods of the order of a decade. Just by applying the 10^-7 factor for the proportion of radiation and the 1/10 factor for the effect in the N or S direction we can find that the solar core will be moved by about 0.01 km N and S over a few decades. That may not sound like a lot, but the temperature gradient of the Sun is about 20 degrees per km and so that small movement should cause variations in the temperature at the poles of around 0.2 degrees. Remember also that radiation produced is the 4th power of temperature so this would cause a variation in radiation at the Sun's surface of about 0.015%.

Up until now I have only addressed the gravity effects on radiation. However teh effects on relativistic matter are also important. This may be a controversial matter as regards GR and some experts disagree. However Birkhoff says that it also applies to matter.

Anyway, the matter component may be several orders of magnitude higher than the radiation component. I think most important is that electrons have much higher velocities than nuclei in the solar core and so are more relativistic. Therefore there will be additional differential acceleration* applicable to this.

* By differential acceleration I mean that the centre of the sun is affected more than the surface due to its differing relativistic content.