[_qwfv]

There's no such thing as 'nudging' it into the sun. If you don't push hard enough, it will enter an orbit that coincides with earth's. And to push it hard enough you basically have to get it going away from earth at the speed earth orbits around the sun, which is quite fast.

Anything less, and it will be in an orbit that floats close to the sun then floats back up towards earth, more or less forever.

[fullstop]

I think that we're going to need a bigger space elevator, then.