2024 YR4 is going to pass earth 20.6 Lunar distance away in 2028, then pass less than 1 lunar distance from earth in 2032. How can we slow it down with a mission in 2028 so that when it comes by in 2032 we could capture it in our orbit?
The 'why' is because of the resources from the asteroid, they could be used to build a radiation proof, micro-meteor safe space station.
According to its Wikipedia article,
The mass and density of 2024 YR4 have not been measured, but the mass can be loosely estimated with an assumed density and assumed diameter. Assuming a density of $2.6\,\mathrm g\,\mathrm{cm}^{-3}$, which is within the density range for stony asteroids such as 243 Ida, with an assumed diameter of 55 m (180 ft), the Sentry risk table estimates a mass of $2.2\times10^8\,\mathrm{kg}$.
Current estimates have it on an apparent trajectory that’ll get it up to around 17 kilometer per second near impact.
So, it has approximately $3.74\times10^{12}\,\mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-1}$ of momentum and approximately $7.8\,\mathrm{Mt}\,\mathrm{TNT}$ worth of kinetic energy. Compare the former to the $400,000\,\mathrm{kg}\times 8,000\,\mathrm{m}\,\mathrm{s}^{-1}=3.2\times10^9\,\mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-1}$ of the ISS, and compare the latter to a fairly-large fusion bomb.
To slow it down by ten kilometers per second to get it into orbit, we’d need to put around $6\,\mathrm{Mt}\,\mathrm{TNT}$ of kinetic energy into it (assuming it passes tangent to the low-Earth-orbit that we want it in and can do this in an impulsive maneuver), and we do not have the capacity to efficiently transfer that much energy to it without vaporizing it.
As awesome as an asteroid-ship is, we’d be riding it, not capturing it.
