That's an oversimplification, and it misses reality.
The Sun is moving relative to its previous position. It isn't fixed. Likewise, the Earth is moving relative to its previous position, it isn't fixed, either.
The Light that we on Earth see from the Sun is actually from where the Sun was located 8.3 minutes ago. Yes, both the Earth and Sun have moved in tandem during those 8.3 minutes, but that doesn't mean that the Earth and Sun are in a "fixed" location. The *angle* at which we see the Sun from here on Earth is distorted from where the Sun is actually located.
Instead of seeing precisely where the Sun resides, we see where the Sun was located 8.3 minutes ago (some 78,000 to 300,000 miles away, depending upon how fast one can show that the Sun moves).
If *both* the Sun and the Earth are moving Northward at 157 miles per second, even as the Earth simultaneously revolves around the Sun, then the Light that we see from the Sun will be from the location that the Sun was at 8.3 minutes ago, which is 78,186 miles *SOUTH* of its actual current position (because it takes Light 8.3 minutes to reach the Earth).
So forget Gravity. Until we can agree that:
1. The Sun is *moving* relative to it previous position,
2. Light takes 8.3 minutes to travel from the Sun to the Earth
Then we aren't ready to discuss Gravity.
We have to be able to agree that the Sun is moving and that Light takes time to reach the Earth before we can go any further in this debate, and that's because we have to build a framework wherein we agree or disagree that we are viewing the Sun in its old location of 8.3 minutes ago.
1. The Sun is *moving* relative to it previous position,
There is no such thing as absolute motion. If we don't accelerate the sun, then I am at liberty to choose a coordinate system in which the sun is at rest. So no, the sun does not move, according to my choice of coordinate system...and your arguments have to work in that coordinate system.
Forget the sun for a moment. Consider only the earth-moon system. Although the earth is in motion (around the sun, etc.) the moon manages to keep up with us. We never outrun the moon, even though, from your viewpoint, the moon should be struggling to stay in orbit around a runaway target.
I think the answer to this awesome problem is that the two components of the earth-moon system are both in orbit around a center of gravity. And that is what orbits the sun. Likewise, the earth-sun system has a center of gravity (probably within or very near to the sun) and that is what is roaming around the galaxy.
As always, if I've goofed it up, Physicist or someone else who knows this better than I do will straighten me out.
I thought you had it at 18 seconds...
Aberration of starlight
Displacement of the apparent path of light from a star, resulting in a displacement of the apparent position of the star from its true position; discovered by the English astronomer James Bradley and explained by him in 1729.
"The phenomenon is caused by the orbital motion of the earth; in the same way, vertically falling raindrops appear to fall diagonally when viewed from a moving vehicle. The true path of light from a star to an observer is along the straight line from the star to the observer; but, because of the component of the observer's velocity in a direction perpendicular to the direction to the star, the light appears to be traveling along a path at an angle to the true direction to the star.
"Thus, in order to observe a star the central axis of a telescope must be tilted as much as 20.5 (seconds of arc) from the true direction to the star, the exact amount of the angle depending on the direction to the star relative to the direction of the earth's motion in its orbit. Because of the earth's orbital motion, the stars appear to move in elliptical paths on the celestial sphere. All these ellipses have the same semimajor axis, 20.5 of arc, a value known as the constant of aberration. The tangent of the constant of aberration is equal to the ratio of the earth's orbital speed to the speed of light."
This is all elementary and well understood. Attempting to apply it to the Sun merely shows that you have no understanding of the initial answer: that General Relativty has been shown to completely and fully "null out" the aberration of gravity.
--Boris