I am really not sure what the consensus is on the speed of gravity. From what I have seen and read, it appears to me that it is instantaneous over a distance, otherwise things would not work the way they do. From my understanding of the warping of space-time, it would make sense if it were instantaneous because space-time is already warped. Is it better to think of gravity as just there, as opposed to something being given off by a mass in all directions like light?
My question is: Do orbital dynamics support an infinite "speed" for gravity to propagate. I am imagining the Earth and Moon system here. For the moon to keep its stable orbit around a moving body, would the speed not have to be instant for it to work? Lets imagine the Earth as sitting still, or not orbiting a star. In this case, a moon orbiting stably would make sense. Now add the Earth moving in a circular orbit around the Sun at a velocity. Why wouldn't the moon's orbit slowly "fall behind" over time and eventually break off and lose its orbit from Earth?