I think there are many things to ponder in this proposal:
https://www.siliconrepublic.com/machines/analemma-tower-asteroid-skyscraper
Recruiting an asteroid
According to detailed plans revealed by New York-based firm Clouds Architecture Office (CAO), Dubai could one day build a gargantuan skyscraper that would actually float in the above skyline.
How would it do this? As it turns out, CAO is looking to outer space as the platform to hang the building from – more specifically, a passing asteroid.
The Analemma Tower would be a Universal Orbital Support System, built in Dubai due to its specialisation in extremely tall buildings – but this would not be its only location.
Once the engineers have sorted out the small problem of trying to get a huge asteroid into orbit over Earth, a high-strength cable would need to be affixed by astronauts, and then lowered to the Earth to be attached to the building.
Although it sounds like an idea thrown together as an April Fool’s Day prank, CAO has revealed detailed schematics showing how the orbital mechanics of such a skyscraper (or ‘Earthscraper’, in this case) would travel across the globe.