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Yes, drop a large enough rock from, say, orbital height and there might be zero carbon emissions going forward.

For a rock to extinguish all life on and in Earth from an orbital drop it would have to be quite large. I suppose Jupiter would be big enough.

Just human life would do, not all life. But just a drop wouldn't have the relative speed of most asteroid impacts.

You just invented block cave mining https://www.e-education.psu.edu/geog000/node/911

It's been in use for a long time and is great for fragmenting large rocks and boulders. It does still need grind after the main fragmentation is done.

SAG Mills use the same concept to grind rock to a finer level. Most of the abrasion is rock-on-rock inside the mill.

To use gravity, you only have two options:

1. Knock things down that are already high up and hope they break at the bottom. Or,

2. Haul things up and then knock them down.

#1 only works in an extremely limited number of cases and gets exhausted quickly. #2 spends more energy hauling up than it gains.

As long as it's not a Sisyphean task.

"Join my asteroid bombardment startup...."

/s