[z3n]

So basically, we are going back to Newton in the tower. I think it's different because at the point in the experiment before both objects are released they are being held up by someones hands rather than orbital velocity.

Now can we bring in questions of drag? If you don't just have an asteroid but you have a long 'skyscraper', even if it's exposure to atmosphere at that altitude is relatively nominal, because of it's increased surface area, you may have to nudge your geosynchronous altitude to compensate?

[central_va]

Will it have a Denny’s and a casino?

[Purdue77]

Nudging to a higher orbit won't help. The purpose of the altitude is to synchronize the orbit to the rotation of the earth. If you add a drag on the asteroid (due to atmosphere and gravity pull on the building) the drag is a force that will alter the orbit over time unless you do something to compensate. Leaving things alone isn't an option. Letting the drag change the orbit affects many things, such as the height of the building over the ground, the sychronicity of the building relative to its intended path, the period of the orbit, and the velocity of the orbit.