FWL_Engineer said:Adam, great Maths mate, but there are a couple of flaws in it. Firstly, most NEO's have an average density of around 2.8g/cm-³, however the greatest flaw is the in the momentum calculations.
Firstly, actually slowing a body down in the solar system is far easier than you might think, as the Sun's and Earth's gravity will work for you to rob angular momentum from the object, and if the orbital calculations are done precisely enough, then you can get Earth to slow the Apophis's orbital velocity by over 90% alone.
Well, I'm only a bit off: 3.3 to 2.8, not that bad!
With regards to gravitational braking: here is how you would do it:
First you would have to ensure the asteroid ends up IN FRONT of the Earth, and slightly outside the Earth's orbit around the Sun. (luckily, this would get you a prograde orbit!). That's OK.
But then you run into a problem... "gravity assists" merely translate angular momentum. It is not "free energy". You can't use one to get an object into an orbit around another body. Their only use has been with interplanetary probes, you swing it around a planet and shoot it off at a different angle. Therefore saving propellant. But the TOTAL momentum of the asteroid remains the same. You would still need to supply 100% of the impulse required to slow the asteroid to earth-orbit velocities, so loadsa rockets. A stable orbit is just a gravity assist, after all. But satellites don't go shooting off at tangents with all the free energy
I still think an easier task would be to place it in an orbit further out, which would require less of a momentum change. It wouldn't be geostationary, but at least that means we can all see it! Dunno about you but I would be pi**ed off if the Earth got a new moon that I couldn't see without flying thousands of miles!!! On the upside, that link reckons London will be a good place to see the asteroid scoot past in 2029.