Didn't read it all, but the nature of the proof is pretty obvious in the initial diagram, and yes, it (speed-of-light gravity) would seem to inject energy into a closed system, with action not being balance by an opposite reaction.

The physics of instantaneous gravity seems flawed as well since it requires a simultaneity that is undefined without a frame. So OK, the frame of the mutual center of gravity is used, but that means that in different frames, the force on one object from another is different, which is contradictory. How can object X pull on me in different directions depending on reference frame? It could be measured, and the direction of force be used to determine an absolute reference frame.

Bottom line is I think your physics is off in the SOL example that spirals out, but I cannot yet put my finger on it. Such a simple proof must have been critiqued by the physics community. — noAxioms

That proof has never been critiqued by the physics community - because the physics
community does not comprehend critique any further than if they speak out of turn
and out of pecking-order they'll get their funding cut.

You cannot put your finger on it because you are looking for sophistic solutions.
The simple answer took a much longer complex route to arrive at than is presented.
By not reading the full argument, you sentence me as a witch - the simple is wrong
because its simple and the complex is too complex for you to bother with.

To answer your first point, the objective frame of reference will always be the sum of gravitational fields.
As regards the binary - the barycenter is very close to it as more distance objects alter this by little.

The problems start right there. Einstein did not propose gravity to propagate at all. Gravity waves, yes, which act as the particle equivalent of excitations in the quantum field, but gravity itself (the sort that attracts two orbiting stars to each other) is just an effect observed by spacetime being curved by the two masses. There are no gravitons involved, and no propagation of anything. — noAxioms

Wrong.
Einstein claimed gravity propagates at lightspeed.



The entire point of LIGO was an attempt to try and prove this,
and even though they did not, Weiss was given the Nob prize for claiming just this.
Even a basic reading of the subject should clarify it.
Although it is a popular internet rumor that there is no propagation of gravity at lightspeed,
the formal articles all say there is.

Or do you reckon that the most widely read book in astrophysics reprinted more than
a million times, just plain 'got it wrong' and nobody ever noticed, hmmm?

You have a copy of Hawking's little book?
Checked that yourself have you?
I suggest you read my articles a little more closely old chap.
(After you flip through to p.94) - But that was a scan from the printed text, innit?

We measure moving objects by their light emissions, with the light traveling at the speed of light. If the two objects are on the arc of a circle; same distance from the observer, they will appear to be synchronized. If they are at different distances, they will never appear simultaneous, unless one of the sources generate its light signal, with the correct time delay.

In terms of the mass of objects, we do not measure the mass directly. The mass or material is inferred from the energy signal; bending. Conceptually, two masses can synchronize at any distance, but since we observe them indirectly through their energy signals, human perception of the energy middleman will be the rate limiting step to observing simultaneity.

Say you traveled at the speed of light, but in a very tight 3-D spherical orbit, so you can see the entire universe at the same time. According to SR, the size of the universe will appear to contract to a point-instant. This means, the entire universe will appear synchronized at the speed of light since there is no time delay between overlapping points. Perception that there is no synchronization is an artifact of inertial reference using middle man energy signals to define the universe.

It is sort of a magic trick, where the audience is distracted by the middleman.