If the idea of gravity propagating at light speed is a requirement of relativity, then it's time relativity was dropped. Gravity is known by experiment to propagate either instantaneously or close enough thereto that our best instruments cannot tell the difference.
Tom Van Flandern's page on the topic at Metaresearch notes that:
By contrast, gravitational forces are large, readily detected, and control the dynamics of most of the visible universe. Gravimeters easily detect the gravitational force from, and motion of, a person entering a room, for example. The propagation speed of gravitational force is bounded by six experiments to be much faster than the speed of light.
[[5]]. For example:
- In 1825, Laplace determined that the minimum speed of gravity consistent with observations was at least 10 million times the speed of light, c.
- Modern, high-precision solar system observations show that the direction from which the Sun's light comes, and the direction toward which the Sun's gravity pulls us, are not the same. The former is retarded by the time it takes light to travel from Sun to Earth, 8.3 minutes; and the latter is not retarded by any detectible amount.
- Eclipses of the Sun by the Moon occur about 40 seconds before the time of the Sun's maximum gravitational pull on the Moon. The delay indicates that light and gravity do not have the same propagation speed.
- A 1997 laboratory experiment by Walker & Dual showed that gravitational signals propagated much faster than light signals.
- Binary pulsars (with large masses and speeds) show that the speed of gravity must be at least 20 billion times the speed of light.
Van Flandern stops just short of calling Kopeikin an outright fraud.
And that's *precisely* what we've been discussing on this thread.
The person would be so kind as to enter the room 100 times so we can do a least squares analysis.