I have a question about the precision of predicting the movement of objects in space (which I believe fall under physics and not space exploration). While I suspect the main limitations here are measurement and mapping, I do not know whether there are also theoretical objections to the following scenario:
With present-day technology, I set up a mass driver on a small asteroid. This has the ability to throw rocks in any direction. I know the composition (density) of the entire asteroid to the same detail that I would on Earth. I follow up to buy a 100x100 km plot of land in Sahara. Will I be able to steer the asteroid with sufficient accuracy to hit the 100x100 km plot of land? To avoid course corrections arbitrarily close to Earth, let's say I am not allowed to run the mass driver any closer than the orbit of Mars. I have not specified the size of the asteroid, but it should be big enough not to burn up in the atmosphere (presumably it is made of very valuable material) and small enough not to cause a disaster when impacting Earth.
If this is not possible, is it due to:
insufficient knowledge about other atmospheric bodies that will impact the trajectory of this object?
insufficient calculating capacity to know how all known bodies will affect the path of this object?
impossibility of running a mass driver with sufficient accuracy with present-day technology?
uncertainty in weather patterns, atmospheric density or the path/orbital speed of the Earth?
some other factor?