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 not by an amount that would be measurable on human timescales, even though the speed of light is much faster 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.

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.

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 not with an angular velocity that linearly increases with time). 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.

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 not by an amount that would be measurable on human timescales, even though the speed of light is much faster 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.