Re: What would happen if men were to heavily mine a small moon.

Q. What would happen if in the distant future men were to very heavily mine a small meteorite or even moon. Would it be possible to mine a small moon enough to actually reduce its gravitational pull enough to affect working conditions etc.

This is really more of a question about technology than it is about science. If your technology supports it, you can mine any rocky body enough to significantly reduce its gravity. Consider the sort of thing we are marginally capable of right now. We could set up mining on a typical small asteroid, say 1 km in diameter. The volume of the asteroid is:

V = 4/3 * pi * r^3 = 5e8 m^3

M = 1.5e12 kg.

G = m / r^2

G = 2.5e-13 / (7.8e-5)^2 = 4e-5 times Earth's surface gravity.

In other words, a mass weighing 100 kg on Earth will weigh about 4 g on the asteroid. That doesn't sound like much, but it's probably enough to affect how the mining operation works. A big mining machine that weighs tons on the Earth is still pretty heavy even if it weighs 20,000 times less.

There are pit mines on the Earth that have had more material removed from them than the volume of our asteroid. The Bingham Canyon Mine in Utah has about 5e8 kg removed every day; in ten years of operation it clears the volume of a 1 km diameter asteroid.

Much larger bodies could be mined as well, but since the volume increases as the cube of the diameter, there will be vastly more material to remove before the surface gravity is significantly impacted.