Thats the coolest part, ie the old thing about a chain only being as strong as its weakest link, and a chain of sufficient length couldn't even hold a feather due to its own weight.

The CNT's (if near perfectly atomically aligned) and give them an INSANE tensile strength, some numbers I just googled puts steel at about 620 MPa (0.62 GPa) whereas the CNT's that have been made are pushing 80 GPa.

Obviously something this big is already gonna be a multi-governmental collaboration, but all you need then is to find the easiest reasonable sized meteor to DART our way, and catch that bitch on the way by.

For the atmosphere part, it would have to be an entirely geostationary orbit, and so really you would have the same winds as expected on skyscrapers (plus a bit). All this the tensile strength has more than enough wiggle room for.

Material costs aren't too bad too considering its nearly a hydrocarbon, and the strength only requires a fairly thin cable - in equivalent terms imagine the material for a road as long, we've got millions of km's of them, 100 is easy