How does GRT eliminate the influence of the gravitational delay?

TonyYuan

Gravitational Fields and Gravitational Waves
Registered Senior Member
https://photos.app.goo.gl/vxxtESuy1upGdsHT8
As shown, we have constructed a very simple Sun-Earth model. If the speed of universal gravitation is equal to the speed of light, the gravitational force of the sun will reach the earth with a delay of 8 minutes, then the gravitational force of the sun on the earth will come from S1 instead of the real position S0, so there will be a component F1 opposite to the revolution velocity of the sun. Under the action of F1, the earth will move to the left as shown in figure (a). Finally, Earth would follow S1, as shown in figure (b), which is inconsistent with the real solar system.

How can we interpret this Sun-Earth model in terms of GRT? That is: under this gravitational delay, according to the calculation of classical mechanics, the orbits of the planets in the solar system will no longer be stable. How does GRT eliminate the influence of this gravitational delay?

Tony;

The drawing you showed has no scales, so is difficult to understand.
Here we begin with a spacetime graphic on the left.
The sun S is the ref. frame with earth E orbiting S in a spiral pattern as depicted in
your animations. The gravitational energy GE (blue) is assumed to continuously radiate from S in a spherical pattern at light speed, (a cone without the 3rd dimension). The planets are assumed to orbit in the xy plane. The radius 0x =149 km, ct=8 light min.
Some perspective.
The vertical time axis was modified by the factor c, otherwise light propagation would be a horizontal line and offer no analysis for near light speed phenomena. The distance um (light sec) is 300 million times greater than the time um (1 sec). That's why prior to the Newton era, light was thought to propagate instantaneously.
The modification results in light speed shown as a 45 deg line. All speeds for human activities excluding light occur in a tiny cone that is indistinguishable from the ct axis.
The x axis is object motion vt, and the ct axis is light motion ct. The slope of a line is then vt/ct or speed v/c. The most common mistake is trying to read the Minkowski graphic like a 2D geographical map. There is nothing moving along any line within the
blue light cone. The lines are histories of positions.
The conclusion.
The GE is moving in the x direction, as shown at the bottom.
What is necessary now is to remove the scaling by c to restore the real world perception on the right.
The GE will charge the space simultaneously with the arrival of E, which will be directed toward S. There is no delay, and gravity is perceived to act instantaneously.
Also the spiral path for E will be much looser than those in the animations. Consider the distance E moves in 8 min. vs 360 days for an orbit!

Here's a brief explanation in words. It's quite complicated. If you want the maths, you'll need to learn GR properly:

Does Gravity Travel at the Speed of Light? (ucr.edu)
The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the newtonian result.
Also, the cancellation is nearly exact only for constant velocities.

Please give the mathematical derivation process of the above conclusion.

In my opinion, the above two sentences are equivalent to this sentence:
The net result is God appeared, and the propagation delay was successfully cancelled by God.

Please give the mathematical derivation process of the above conclusion.
This is the point where you'll have to hit the textbooks, I'm afraid.

This is the point where you'll have to hit the textbooks, I'm afraid.
Get your math proof! Don't just talk.