How much energy to destroy the crust of a planet?

In the Star Trek: Deep Space Nine episode The Die is Cast. A planetary bombardment scene occured where 17 shots was stated to have destroyed 30% of a planet's crust. Now obviously that's a HUGE amount of firepower, but it's not unrealistic for Star Trek as since the pilot episode of the original series they stated they had enough firepower to blast a continent.

So what kind of firepower are we talking about here?

Specifically if the entire crust were destroyed right down to the mantle. As in what kind of energy levels are we talking about (preferably in tnt equivalent) would be necessary to destroy completely or severely extrude the crust of 30% of a planet's surface area? What about the entire planet?

To make things easier lets just assume values for Earth.

• John, for a quantitative answer, you'll have to provide a bit more information. What do you consider "destroyed"? Heating it to 100C ought to kill off 99.99% of life in the region. Melting it would kill all living things on that crust. Vaporizing it is probably overkill. Doing any of these will cause huge global weather changes. Also are we talking just continental crust or the oceanic crust too (I ask because getting to the oceanic crust requires vaporizing all that water too). – Jim2B Apr 16 '16 at 17:54
• Due to the wonderful nature of Star Trek having a budget sfx team. The planet in question had a venusian style atmosphere that conveniently hid the exact nature of the destruction, all the viewer saw in the shot was huge waves of presumably the disturbed atmosphere itself propagating across the surface. However for this question I'm assuming complete and total vaporization right down to the mantle. And the planet most likely didn't have any oceans. – John K. Fitzgerald jr. Apr 16 '16 at 18:14
• This still feels like it's not very well specified. Right now the answer could be: Work out the mass. e=mc^2. Job done :) – Tim B Apr 16 '16 at 18:18
• At the very least I'm trying to find out how much energy would be needed to vaporize a planet's entire crust right down to the mantle. If e=mc^2 is enough to figure that out, then what would be a ballpark mass for the earth's crust? If it makes it easier I'm looking for energy in terms of weapons being fired at a planet. My guess so far is a blast around 10 petatons tnt equivalent. – John K. Fitzgerald jr. Apr 16 '16 at 18:31
• @TimB Would you not need the heat capacity of the crust though? – Bellerophon Apr 16 '16 at 20:50

The always helpful Atomic rockets Boom Table has the following information for us:

6.6 × 1026 J, 158 Pt: Energy required to heat all the oceans of Terra to boiling

3.2 × 1026 J, 77 Pt: Energy required blow off Terra's atmosphere into space

7.0 × 1027 J, 2 Et: Energy required to vaporize all the oceans of Terra and dehydrate the crust

2.9 × 1028 J, 7 Et: Energy required to melt the (dry) crust of Terra

2.1 × 1029 J, 50 Et: Earth's rotational energy

1.5 × 1030 J, 359 Et: Energy required blow off Terra's crust into space

(remember, 1 Pt = 1 000 000 gigatons; 1 Et = 1 000 000 000 gigatons)

Just to put this into perspective, we should consider:

5.5 × 1024 J, 1 Pt: total energy from the Sun that strikes the face of the Earth each year

3.9 × 1026 J, 92 Pt: total energy output of the Sun each second (bolometric luminosity)

So to seriously destroy a large part of the planet's crust you would need to somehow generate and deploy a large fraction of the energy of a yellow dwarf star.

In real terms, it seems very unlikely that a ship would be able to do anything like this on its own. The only plausible mechanism would be the ship opens a wormhole to the closest star and directs the star's energy against the planet's surface or better still somewhere under the crust. Just don't stand too close....

• There's a good answer in exactly the energy units I was looking for. 359 exatons. Now the bombardment in question only destroyed the crust over 30% of the planet's surface area so that would make that bombardment's yield at 107.7 exatons. I realize that it's not practically plausible, but it is science fiction and the nature of Star Trek power generation and weaponry makes them very good at destroying matter efficiently. – John K. Fitzgerald jr. Apr 16 '16 at 23:57
• God bless the internet, where "Energy required to blow off Terra's crust into space" can be found on a webpage titled "Useful Tables!" – Cort Ammon Apr 17 '16 at 0:31
• @Cort Ammon: Well, considering that it did happen... At least according to the fairly well accepted 'big splat' theory of the Moon's formation. – jamesqf Apr 17 '16 at 5:26
• Don't forget that a Photon Torpedo only generates $2.7 \cdot 10^{17} J$, so it's going to take a rather large number of them (something like $5 \cdot 10^{13} \times 0.3$ of them) to do the job. – Jim2B Apr 17 '16 at 5:44
• @Jim2B Well obviously that isn't true since a handful of them in the episode mentioned above did the feat of destroying 30% of a planet's crust. I prefer to gauge fictional weapons off of their observed feats rather than just blindly listening to some number in a tehcnical manual. – John K. Fitzgerald jr. Apr 26 '16 at 2:27