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Analysis / Colony Drop

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Note that in real life, the colony and moon version of this is very, very difficult. It's nearly as hard to take something out of orbit as it is to put it in in the first place, as all the momentum must be shed. The energy necessary to do this is actually more than will be released in the collision. Note that most of the force would come from Aerobraking in the atmosphere, so it’s not all that hard for something in low earth orbit where "stationkeeping" burns are required to to keep the object in orbit.

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One case where this would work would be if the object being dropped is in an extremely eccentric orbit (or just a very distant orbit, such as Earth's Moon, which would require little delta-V to convert to an extremely eccentric orbit), as the object's orbital speed at or near apoapsis would be extremely low, such that even a small amount of delta-V would produce a large change in trajectory, especially around the opposite end of the orbit (you know, the end that, with a little tweaking, would intersect the planet).

Even if a planet or moon-sized object does get sent on this sort of collision course, it will likely break apart under the force of gravity once it gets too close and passes a threshold called the Roche Limit. This will still have world-ending consequences — using the Moon as an example, tides will get thrown completely out of whack and cause widespread flooding and a host of other natural disasters — but an actual impact with planet Earth is the least of your worries.

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