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
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
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