Remember that question someone asked in here – does gravity work at the speed of light, or instantaneously? Well, you can't ever directly measure the answer unless the sun disappeared by magic.
Actually, it has been measured. Astronomer Tom Van Flandern measured the "aberration" (angle) between the Sun's light and its gravity. I made a few animations for him to explain astronomical concepts, and one of the animations was aberration. Another was an animated version of "what if the Sun magically disappeared?"
I'll be dumped on by all the Professional Physicists™ for saying this (they can't abide dissent), but we don't know what
gravity is. In fact, we're no further ahead than Newton who did not explain gravity
, he merely quantified it. And that's all we can do today. (Yeah, yeah, I know. Einstein and warped space, but all that does is shift the question of gravity, it does not explain it.) The answer is that gravity—whatever it is—is faster than light.
The chances of it hitting one of the basketballs is about the same as the odds of ship hitting a star: effectively zero.
And if we look at the flip-side of that analogy, how do the starships so unerringly find the destination stars over such vast distances?