Gravity propagates instantaneously to within our ability to measure it and that has been known for several centuries. Every time you take five steps you are sending a gravitational message out into the cosmos and somebody on the far side of our galaxy with a sensitive enough instrument could read that message and it wouldn’t take him thousands of years to do it; he’d probably be able to read it inside of a second.
I responded to this misconception in post #287. Gravity travels at or near the speed of light as far as experiments have determined. If you haven't studied quantum mechanics, electrodynamics, and optics then you should STOP NOW before you dig yourself a hole. The same bad logic that people use to say that gravity travels faster than the speed of light also works almost identically for electromagnetism, a force ~10^40 times stronger. And I don't think there is any doubt that electromagnetic interactions work at the speed of light.