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You are stating the analogy just fine, but the limits of analogies come into play here because the sheet has no propagation speed and it has no movement of its own, either (nor does the big ball at rest in its center).

Those are the aspects of the situation that are analogous to the sun.

The sun, insofar as it is not subjected to accelerations, is at a fixed location in its own reference frame. The sun's gravitational field, as long as the sun hasn't undergone an acceleration for more than 8.3 minutes, is fixed to all points in space, at least as far as the Earth's orbit is concerned. The field, like the sheet, does not need to propagate; it's already where it needs to be. The Earth will "see" the same field at every point, regardless of how fast it's moving (neglecting the "gravitomagnetic" effect, which is a known relativistic correction that is vanishingly small).

Should the sun undergo an acceleration (or, God forbid, disappear), the changes in the field will propagate from the sun outward. These changes are gravitational waves, and they propagate at c. Again: waves propagate, fields do not.

The situation is exactly analogous to the electromagnetic field vs. electromagnetic waves. The same geometrical argument applies. Van Flandern now says that while electromagnetic waves propagate at c, electromagnetic fields propagate infinitely fast. Whatever. It's like saying that while cars drive at finite speeds, the road goes infinitely fast. I suppose that's one way to describe it...just not a very useful way.

(I had promised myself not to respond to this Van Flandern crackpottery any more, but RadioAstronomer has inspired me. For the future, I'll put together a boilerplate response.)

"The sun, insofar as it is not subjected to accelerations, is at a fixed location in its own reference frame. The sun's gravitational field, as long as the sun hasn't undergone an acceleration for more than 8.3 minutes, is fixed to all points in space, at least as far as the Earth's orbit is concerned."

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.

That's all well and good, but it brings you full circle; we can no more imagine the static state than we can the infinite range.

The very presence of objects of mass construe the field while they constitute it.

Can we agree that, in the absence of mass there is no gravity and in the absence of heat there is no light?

We have all marveled at the art of the juggler, his balls cycling their silent paths, mesmerizing us as we watch in fascinated awe absorbed in their motion to the point where the juggler disappears from our view; but, take away the juggler and the balls all fall.

My point, I guess, is to always keep your eyes on the juggler and let the balls fall where they may.