Speed of gravity according to Laplace

Question

We find first of all that it requires us to assume that gravitational propagation is not instantaneous, but occurs with the speed of light. One might think that this is reason enough to reject the hypothesis, since Laplace demonstrated that this cannot be the case.3 In reality, however, the effect of this propagation is compensated in large part by a different cause, in such a way that no contradiction arises between the proposed law and astronomical observations.

Paragraph 13 introduction On the dynamics of the electron: Introduction

Einstein's Time Dilation is an Effect of Clock Synchronization

after having adjusted the watches by the optical procedure, we wished to verify the adjustment by the aid of these new signals, we should observe discrepancies which would render evident the common translation of the two stations. And are such signals inconceivable, if we admit with Laplace that universal gravitation is transmitted a million times more rapidly than light?

Laplace proved that the speed of gravity must be million times greater than speed of light,

I couldn't find his proof,

My question is how does he proved this to be true and how was it refuted?

Answer 1

This link seems to have a complete explanation. In summary, there was some challenge to explain how the Babylonians had measured a slower moon-orbit angular velocity than the "modern people" of the 1700s. Which is, I believe, not true - the moon's orbit is slowing down not speeding up - it seems people at that time were still struggling with the concept of measurements coming with errors. But in any case Laplace explained this using the perturbations to the earth-moon system due to other planets.

But Laplace also considered another explanation, which it seems he didn't really believe to be likely. He made a model where gravity had a finite propagation speed, and in this model the moon moves toward the Earth and speeds up over time. He matched this model to the Babylonian observation and got that the speed of gravity is 7 million times the speed of light. Incidentally, gravity does have a speed (the speed of light), but it doesn't give rise to this phenomenology (okay fine, gravitational waves cause orbiting bodies to coalesce, but the orbital period only decreases by $4\times10^{-19}$ seconds per 1000 years because of this, even though the speed of light is much lower than Laplace's estimate). So it seems that this oversimplified explanation of Laplace's speed-of-gravity-measurement is not very correct. Considering Laplace didn't think this was the best hypothesis, and the model wasn't correct for the consequences of a speed of gravity, and the observation it was trying to explain was also wrong.