it is called gravitational wave. The GGP strangely didn't mention it. The gravitational wave is a strange creature as it is a disturbance of space-time, thus question of its speed, distance by time, becomes a bit murky - like what distance? what time? - depending on how you answer the questions (and don't forget, talking about astronomical scales we start to face astronomical factors like noticeable spacetime expansion) - you get corresponding result.

>>"fall if you are dropped" is just being continuously emitted by the Earth, including before the object was dropped.

it is gravitational field of Earth. If Earth were to move with acceleration (as any movement without acceleration is as good as not moving at all by suitable choice of coordinates) the object would start to fall toward previous "retarded" location of the Earth, until the gravitational wave caused by the accelerated move of Earth "updates" the gravitational field at the position of the object.

>The question becomes what if the object moves - how long does it take to notice the new location of the gravity.

a moving object gets instantaneous value of gravitational field at its new position (while this value may be already "obsolete" like in the above mentioned accelerated movement of Earth)

Yes, I know, but that's not what the quoted reddit comment claims:

> To the absolute limit of our ability to measure it ... when an object is dropped, it begins falling instantaneously. ...This is fairly earthshaking, really. Because it implies that somehow a "signal" of some kind is getting from the ground to Wile E. faster than the speed of light. Which is supposed to be impossible.