Throwing Stuff Down A Mineshaft

I have a couple of questions, generally, about a few things generally discussed in this thread.1. What effect would the rotation of the Earth have on the falling goat? Wouldn't the poor thing keep banging on the sides of the hole all the way down, then all the way back up, then all the way back down again, then all the way back up again again, then . . . . (making myself dizzy so stopping now).2. Re Dyson spheres: I'm confused about whether there's no gravity at every point inside the sphere. Gravity operates according to the inverse square law, no? Therefore, it seems to me that if you are closer to one side than the other that the gravitational pull from the closer side would be stronger and, thus, draw you to that side. I'm quite sure that people who know lots more about physics than I do have worked this out and I'm just wrong, but if someone could explain it to me, I'd appreciate it.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat

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I'm not positive about this, but I think that the rotation of the Earth wouldn't have any effect. That is, the goat is on the Earth already (that's where it jumps from to get into the hole). So that would mean the goat has all the rotational momentum and motion of the Earth.

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Well, here's where I'm running into trouble. Assuming the hole is at the equator, when the goat first goes in, he has a speed of appx. 1,000 miles an hour as a result of the Earth's rotation. However, as he falls, the relative speed of the Earth will drop but his won't. Thus, as I see it, he'll eventually bounce off the side. And, after the first bounce, there's nothing to keep him from bouncing off the other side, and so on.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat