Is this right?

[SAMAS]

From a post on Comic Book Rumbles:

Okay, I'm no mathematician or physicist, so feel free to correct me on this.

In ESB, a turbolaser was able to vaporize an asteroid about as big across as the Falcon was long. Assuming it's 24 meters across, and even if we assume that it's a perfect sphere made of iron (Which it ain't.) it would only take 200 terajoules of energy to vape it, and, since a megaton blast is roughly 4 Petrajoules, destroying that asteroid only took 5% of a megaton.

In other words, a megaton turbolaser would be able to vape a sphere of iron 480 meters across, 200 megatons would be able to vape a sphere 96000 meters across and 200 gigatons would be able to vape a sphere 96000 KILOMETERS across.

But again, no physicist.

Something stinks here, but I haven't actually checked it yet.

[Elheru Aran]

If that's the case, then a hit from one of the Home One's main turbolasers should've been able to fatally cripple Death Star II, by blowing huge chunks out of it.

I don't remember that happening, do you?

[Nephtys]

The megaton -> Joules is right. It's roughly 4 * 10^15 J.
6,260,000J is the vaporization energy for one kilogram of Iron.
The volume of a 24 meter sphere is 7238.2 meters cubed.
7874 kg/m^3 is the density.
Our sphere therefore, has 56,993,586 Kilograms of Iron in it.
To vape it, you need 3.57 * 10^14J.

So that seems to fit with your friend's calculations. I'm slightly rusty, but 'Captain Sarcasm' doesn't seem to be taking into account that one must heat an asteroid to melt it, then vaporize it perhaps. That's what I'm thinking.

Also, 200 megatons won't vaporize a 96 kilometer wide lump of solid iron. The russian 65 megaton nuke sure as hell didn't do that.

[Darth Quorthon]

My guess is that he's confusing diameters and volume. An iron sphere 96000 meters across would be far more than 200 times as massive as one 480 meters across. A sphere with a diameter of 480 meters would have a volume of 57905835.79 cubic meters, and a sphere with a diameter of 96000 meters would have a volume of 463246686327767.1 cubic meters. The second volume divided by the first is 8,000,000. So increasing the diameter by a factor of 200 increases the volume, and thus mass, by a factor of 8 million. So I'm guessing it would take 8,000,000 times as much energy to vaporize the asteroid of 96,000 meters, not 200. If I screwed up please let me know.

[Wyrm]

If I screwed up please let me know.

Nope. That's exactly right. And a sphere 96,000 km across would be a billion times more volumous than the 96,000 m one. Thus, you would need 8e15 megatons to vape such a ball of iron, if the original assertion that "1 MT => vaped 480 m iron ball" is correct.

Of course, a body that big would also have gravitational binding energy, which needs to be tacked on as well.

[nightmare]

If these calculations were true, Earth's combined nuclear arsenal would be able to easily vapourize a planet the size of Jupiter, to say nothing of Earth. He's confusing diameter with volume (plus it's an artificially simplistic premise).

[LaCroix]

Volume of a sphere 4/3 * r³ *Pi
vapourization 6,26 MJ/kg.
Density 7870 kg/m³.

24 meter:
4/3 * 12³ * pi = 7283 m³ -> ~57 million kg -> 3,57*10^14J

A rough 85kt in my book

480 meter: (480/24 = 20 times larger radius)
4/3 * 480³ * pi = ~58 MILLION m³ -> ~455 billion kg -> 2,8 * 10^18 J

Exactly 8000 times (20³) more volume&energy.
This reads to me als roughly 660 mt... -8000 times -Sounds plausible.

96000 = 480 * 200

So a 96000 m asteroid will need about 8.000.000 times more energy 2.2 * 10^25 (I hope, I have the numbers right, I got confused counting all those Zeros ) to go "vape".

Also, remind him that if it was iron, it would be EASIER to vape, since Stone resists much higher temperatures. Claiming it was not iron easyly doubles the energy needed to vape it.