If we took all the firepower humanity has accumulated and planned to properly ‘destroy’ our planet, how much would be destroyed, as in removed as a part of the planet?
Can’t answer your question, but maybe a couple of ideas:
If we wanted to destroy it as in nuke it from orbit, I doubt we’d make much of a dent (the Earth is, after all rather massive), although we’d pretty much wreak havoc with the upper crust for a couple of hundred meters of depth, perhaps?
However, if we deployed the nuclear arsenal of the world in a very clever fashion, and then exploding them in such a way to cause all the super volcanos to erupt at once, I’d imagine we’d do more than just scar the surface. We’d still only be able to remove a small (very small) amount tough (The Earth still being rather massive), but we should be able to remove the tiny bit that counts.
Back-of-envelope calculations:
Worldwide Nuclear arsenal: 5000 megatons of TNT = 2.092 x 10^19 J
Escape velocity from earth= 11200 m/s
KE=0.5mv^2
mass removed = 2 * 2.092 x 10^19 / 11200^2 = 1.6 x 10^11 kg =
.000000000027% of earth’s mass.
This assumes all energy from each explosion is converted directly to kinetic energy, and 100% of the energy is directed away from the surface of the earth.
If I did my math right, that’s the outermost 0.00002 inches of topsoil from the entire surface of the earth.
I think many folks fail to grasp how truly massive the earth is.
Less than the amount of damage Arthur Dent would cause to a bulldozer that rolled right over him.
How many centuries are you willing to wait? One of the easier ways might be to modify the orbit of a comet or asteroid slightly, and set it on a collision course. A tiny impulse might take a while to amplify into a colliding orbit. Would it be a good exercise for some undergraduate to determine the best comet or asteroid to use? And perhaps best would be to first arrange a close pass to the Moon, for a slingshot acceleration.
I don’t know what the best way to change the asteroid’s orbit would be. Build an H-bomb with charge shaping and send it on a space-probe?
(There was a related thread a year ago or so, though that Doper insisted that all life on the planet be destroyed. What’s wrong with you guys? :eek: )
And then we’d be covered in boiling hot mag-ma. Bwa-ha-ha-ha!
That would add mass to the Earth. Some fragments would be ejected into orbit, but they wouldn’t be equal in mass to the impacting body. Earth has quite a high escape velocity. That’s why it’s a planet - it got big enough to accrete smaller objects.
Our options are limited. The total payload delivered to Earth orbit is roughly the load of a single container ship. Here’s a left field suggestion. We could mine as much helium as possible, possibly with widespread fracking, and let it escape into space. Also, we could use electrolysis to produce huge quantities of hydrogen, and release that also. I haven’t done the maths, but I suspect that would be far more effective at reducing the Earth’s mass than trying to blow part of it into orbit.
And it this arsenal were strategically deployed, could the force be enough to slightly nudge the earth out of its orbit? And would it be enough to cause the planet to eventually crash into the sun . . . or escape from it?
Seems like trying to create a black hole is the best option.
Orbits don’t work like that. Even if we could give the Earth enough of a nudge to change it’s orbit, it wouldn’t cause it to eventually crash into the sun. It would just be in a slightly different orbit.
There are whole websites devoted to this very topic.
Does that include the topsoil on top of the oceans, or just from dry land?
OP asks (in the title) how much structural damage we could do, but then specifies that he means, how much mass could be removed from the planet.
Suppose we focus on structural damage, without necessarily removing any mass from the planet. Maybe we could break up the tectonic plates into a larger number of smaller plates that could float around independently. This might lead to deeper fissures in the crust, exposing more of the deeper magma. We could then have extensive and massive earthquakes and volcano eruptions. Maybe enough to wipe out a new generation of dinosaurs (to-wit: us). Does that kind of “structural damage” count?
Pretty much this, though I’d go for shifting Mercury, if possible, and causing it to collide with the Earth. IIRC, Mercury has a huge iron core for a planet it’s size (possibly a remnant of when it was a larger planet that collided with something in the past and blew off a lot of the crust), so slamming that into the Earth would certainly leave a dent. 
Mercury is not a light-weight object. It would be easier to move the Moon, but that also seems difficult.
How about this: start by directing a comet or asteroid at the Earth as before, but instead of colliding it, place it in an orbit where it will destabilize the Moon’s orbit. The Moon gradually slows down and eventually crashes into Earth. That should satisfy OP’s needs. It may take millions of years to crash, but OP didn’t specify a time limit.
The dope, the place of the classic understatement!
What if we dropped a whole lot of nuclear bombs into volcanoes? Would the explosion cause another Krakatoa?
We didn’t really agree on any time limits in the original conversation that lead to the creation of this topic, but the idea was to destroy the Earth by human action in a relatively short time (a human lifespan at most).
Rendering the earth uninhabitable for humans we can manage. Destroying the earth is utterly beyond any technology we have.
This webpage previously linked above spells it all out:
self-replicating nanobots that will eat up the entire biosphere, using the carbon molecules to encapsulate the water in the oceans.