Near Earth Resources with Low Cost Delivery
As of August 2016, the NASA Near Earth Object Program has estimated Orbital Elements and absolute magnitudes for almost 15,000 objects that cross the 1 AU spherical shell that contains Earth's orbit. The rate of discovery is rapid. From those magnitudes, we can estimate size and volume, more than 1E14 cubic meters.
Over a very long time, we arrange impacts between the near earth objects to break them into 50 meter or smaller chunks, and we tag them with milligram-weight laser retroreflectors for high precision tracking. We also use lasers for ablative thrust. We line these up for delivery orbits to the Moon.
Meteorites are about 5% nickel-iron. Assuming a density of 8000 kg/m3, that's more than 4e16 kilogram supply - 20,000 years worth at current global consumption rates; which MUST diminish over time, as we have depleted everything but lower grade iron ores. Heating iron from cold solid to a hot liquid requires about 1 MJ/kg.
We construct a 30 kilometer geodesic grid of 20,000 "smelting tunnels" across the back side of the Moon, deep holes with 100 meter throats and slight bends partway down. Over a very long time, each object is arranged to fall straight down a tunnel at high speed, to impact a melting chamber at the bottom, while a lid is fired over the top to contain impact ejecta. The objects will impact at greater than 2.6 kilometers per second (the squared sum of lunar escape plus orbital velocity), and have at least 3.4 MJ/kg; after an elastic collision into lunar rock, enough energy should remain in the object to melt it.
This would a very long term project, because arranging the impacts and planarizing the material, then delivering it at a steady rate, may require thousands of orbits of the Sun - thousands of years on average. However, the assumption of continued exponential growth into the far future is contrary to every observed system in nature. All growth (at best) follows an S curve, or worst case an bell curve impulse followed by extinction.
Asteroid orbits are chaotic in the long term. Newton's Clock by Ivar Peterson (1993) says on page 189: "Near-circular orbits can suddenly stretch after a few hundred thousand years of placid behavior, becoming so elliptical that they cross the paths of Mars and Earth." See work by Jack Wisdom when he was a grad student at Caltech in the 1970's (thesis adviser Peter Goldreich). 1982 paper in The Astromomical Journal, March 1982, 599-593 and Nature 315 (27 June 1985): 731-733.
Later recent references suggest some Mars-influenced NEOs have Lyapunov times (errors increase by e) of 100 years or less. Steering them into orbits predictable enough to hit the Moon 1000 years from now requires calculating their position, velocity, and future trajectory to better than 100 meter precision now. On the other hand, an intentional centimeter-per-second velocity change today can evolve into the Earth-Moon distance in 1000 years. So, if we can measure these objects to optical wavelength precision now (5e-7 meters), and model and nudge them accurately enough (BIG if), then a 50 year Lyupanov time over 1000 years multiplies that optical error into a 0.25 kilometer error, which can in turn be corrected with another centimeter-per-second velocity change 7 hours earlier.
Deflecting useful potential impactors into the Moon (or Mars or Venus for the potential impactors deemed "useless") will require much continuous measurement and correction for a very long time, but the cost of protection is eternal vigilance.
We can estimate the task with the poor man's space probe - meteorites.