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I was reading a post about space mining, specially lunar mining. I was thinking about what would change in Earth's orbit if we start bringing tons of rocks to it? I mean, in a huge scale. So, would space mining change Earth's orbit in a way to produce any dangerous effects? If the system in question is not a planet/satellite like Earth/Moon, would that change anything? Would bringing tons of rocks from Mars be any different than Moon?

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No, there would be no detectable - and surely no dangerous - changes to the Earth's orbit.

Just for the sake of an argument, imagine that we double our coal reserves by bringing coal from another place - and even some of the precious metals are too expensive to be brought by spaceships at this moment. ;-)

The Earth's coal reserves are something like 1 trillion tons which is $10^{15}$ kg. Let's bring this amount from another celestial body - it's about 10 orders of magnitude less than what we can do now but let's imagine we double our coal reserves in this way.

The Earth's mass is $6\times 10^{24}$ kg, so the coal reserves are approximately $10^{-10}$ of the Earth's mass. Now, if all the extraterrestrial coal landed by a slow speed relatively to the Earth, the Earth's velocity wouldn't change at all; only the mass would increase and the heavier Earth would continue along exactly the same trajectory as before.

But now, imagine that the coal lands at some speed, e.g. the safe speed that the space shuttles used to take. It's about $350$ km/h. If you don't get approximately this low, there's a risk that your coal will burn in the atmosphere.

So if $10^{-10}$ of the Earth's mass has a relative velocity that is $350$ km/h, and let's imagine that all the momentum will go in the same direction - we could make the coal space shuttles land at different places if we wanted - then the velocity of the Earth will change by $350\times 10^{-10}$ km/h which is $3.5\times 10^{-5}$ m/h or $10^{-8}$ m/s. The speed of Earth around the Sun is approximately $3\times 10^{4}$ m/s, so we only change it by a trillionth. Correspondingly, the eccentricity of the Earth's orbit could change at most by one trillionth. We would have a hard time to detect this change.

Obviously, you would need to increase the amount of resources you bring roughly by 10 orders of magnitude (which means by 20 orders of magnitude relatively to what we can achieve today) to produce any threat for the Earth. But even if you brought the whole Moon here to Earth, $7\times 10^{22}$ kg (eight orders of magnitude heavier than the Earth's coal reserves), there would be no significant change of the orbit because the speed of the Moon is approximately the same as the speed of the Earth - they're bound together. Well, the shape of the Earth could change a bit if we tried to incorporate the Moon too quickly. ;-)

You would have to bring a big fraction of Mars to the Earth (Mars is both heavier and has a substantially different speed) to change the eccentricity of the Earth's orbit by a significant amount and I assure you that this will remain in the realm of science fiction for many, many centuries if not forever. If you brought 1/3 of Mars to the Earth, you would also have to build mountains that are 1000 kilometers high - more than 100 times Mount Everest, around the whole Earth. And it would still not be too dangerous as far as the orbital characteristics go. Of course, there could be a danger for the people who suddenly have 1000 kilometers of rock above their heads. ;-)

Your question clearly seems to be an artifact of the unscientific doomsday scenarios that have been presented as science in recent years - e.g. the doomsday caused by CO2 in the atmosphere. Even relatively to the atmosphere, our additions of CO2 are negligible - we're changing the number of molecules in the atmosphere by 2 parts per million (0.0002%) per year. But the atmosphere is just one millionth of the Earth's mass, so our annual CO2 emissions only redistribute something like 2 parts per trillion of the Earth's mass every year. Clearly, all those changes are irrelevant from a "mechanical" viewpoint and they're arguably irrelevant from a climatic viewpoint, too.

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Most of this answer was excellent, but the last paragraph is completely off-topic considering the question. –  Mark Eichenlaub Feb 8 '11 at 22:27
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The answers so far miss the key physical aspect: planetary orbit does not depend on the mass of the planet (see Kepler's laws) because planet's mass is much smaller then the mass of the Sun. This means that even if you double Earth's mass by mining Mars completely, it will stay on the same orbit.

Update: this is assuming that Earth's velocity stays the same, but then, if people will be able to move these enormous masses, they could change Earth's orbit at will.

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My answer has surely not missed this point. I explicitly explain that if the reserves land at zero speed relatively to the Earth, the orbit won't change at all. –  Luboš Motl Feb 8 '11 at 13:45
    
@Luboš: well, we wrote our answers simultaneously. But, to be fair, you only briefly mention it in your detailed answer, whereas I think this is the only part worth answering. Speculations on details of space mining are off-topic for Physics.SE. –  gigacyan Feb 8 '11 at 14:39
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The redistribution of mass due to space activities is very small. To the extent there is any space mining which happens it is that we mine out materials from the Earth and over the last several decades sent somewhere around 10 thousand tons of material into space. Given that the mass of the Earth is about $6\times 10^{21}$ metric tons the mass of stuff we have sent into space is a very small percentage. The perturbation is tiny, Any mining from space is also going to be a tiny perturbation.

Commercial activities in space have been with massless forms, in particular with information. The next possible step might be with solar power satellites. Again this is a massless form. Sending spacecraft into space to mine materials is not likely to work any time in the near future. The Saturn Apollo rocket weighed in at 3000 tons of highly processed materials, which brought back 50kg of lunar rocks. From an economic or ratio of materials and energy in verses materials and energy back this clearly is a loss.

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The cost of the apollo program in toto divided by total kgs of moon brought back would be a very disillusioning "price"! –  Georg Feb 8 '11 at 13:39
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The earth accumulates cosmic dust at about 40 tons per day (according to Wikipedia: Cosmic Dust). This seems to have no effect on gravity and the orbit of the earth around the sun. For space mining to have an effect, the mined amount will have to be significantly larger.

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40 tons per day is 2 grams per person per year. Anything economically significant would be several orders of magnitude more than 40 tons per day. –  Mark Eichenlaub Feb 8 '11 at 13:10
    
And then there's an effect in the opposite direction: thermal evaporation of gases (He, O2?, N2?) into space reduces Earth's mass slightly. I don't have any numbers. Which of those effects might be the larger one? –  Jens Sep 26 '12 at 13:57
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